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Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-03-16 Tianyuan Xu, Shanming Ji, Ming Mei, Jingxue Yin
This paper is concerned with the convergence to sharp traveling waves of solutions with semi-compactly supported initial data for Burgers-Fisher-KPP equations with degenerate diffusion. We characterize the motion of the free boundary in the long-time asymptotic of the solution to Cauchy problem and the convergence to sharp traveling wave with almost exponential decay rates. Here a key difficulty lies
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On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-03-15
Abstract Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn–Hilliard equation. We then analyse the resulting model and prove its well-posedness
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On the Trajectory of a Light Small Rigid Body in an Incompressible Viscous Fluid J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-03-15 Marco Bravin, Šárka Nečasová
In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid body coincides with the background fluid velocity in the limit. We are able to consider the limit when
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Threshold Dynamics of a Degenerate Diffusive HBV Infection Model with DNA-Containing Capsids in Heterogeneous Environment J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-03-14 Yu Yang, Cheng-Hsiung Hsu, Lan Zou, Jinling Zhou
This paper is concerned with threshold dynamics of a degenerate diffusive HBV infection model with DNA-containing capsids in heterogeneous environment. We firstly address the existence of global solutions, uniform and ultimate boundedness of solutions, asymptotic smoothness of semiflows and existence of a connected global attractor for the diffusive model. Then, we identify the basic reproduction number
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Effective Estimation of Trapping/Stability Regions and Bilateral Solutions’ Bounds for Some Multidimensional Nonlinear Systems with Time-Varying Coefficients J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-28
Abstract Assessment of the stability/boundedness of solutions to nonlinear systems with variable coefficients brings long-standing and challenging problems which emerge in various application domains. These problems naturally evolved into more arduous and largely open problems concerned with the estimation of the corresponding stability/boundedness regions. This paper develops a novel approach furnishing
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Curvature Driven Complexity in the Defocusing Parametric Nonlinear Schrödinger System J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-28 Keith Promislow, Abba Ramadan
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Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-24 Elizabeth Carlson, Adam Larios, Edriss S. Titi
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A Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-24
Abstract We consider the initial value problem for a two-component Sasa–Satsuma equation associated with a \(4\times 4\) Lax pair with decaying initial data on the line. By utilizing the spectral analysis, the solution of the two-component Sasa–Satsuma system is transformed into the solution of a \(4\times 4\) matrix Riemann–Hilbert problem. Then, the long-time asymptotics of the solution is obtained
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An Optimal Control Approach to the Problem of the Longest Self-Supporting Structure J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-21 Giacomo Vecchiato, Michele Palladino, Pierangelo Marcati
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Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-15 Jesús Malo, José Juan Esteve-Taboada, Marcelo Bertalmío
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Martingale Solutions in Stochastic Fluid–Structure Interaction J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-02-08 Dominic Breit, Prince Romeo Mensah, Thamsanqa Castern Moyo
We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the literature but only analysed in simplified cases. We investigate the full model with transport noise, where (a part of) the boundary of the fluid domain is randomly
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On a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-01-29 Guodong Liu, Hao Wang, Xiaoyan Zhang
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Applications of Nijenhuis Geometry V: Geodesic Equivalence and Finite-Dimensional Reductions of Integrable Quasilinear Systems J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-01-29 Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We describe all metrics geodesically compatible with a \(\textrm{gl}\)-regular Nijenhuis operator L. The set of such metrics is large enough so that a generic local curve \(\gamma \) is a geodesic for a suitable metric g from this set. Next, we show that a certain evolutionary PDE system of hydrodynamic type constructed from L preserves the property of \(\gamma \) to be a g-geodesic. This implies that
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Vortex on Surfaces and Brownian Motion in Higher Dimensions: Special Metrics J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-01-28
Abstract A single hydrodynamic vortex on a surface will in general move unless its Riemannian metric is a special “Steady Vortex Metric” (SVM). Metrics of constant curvature are SVM only in surfaces of genus zero and one. In this paper: I show that K. Okikiolu’s work on the regularization of the spectral zeta function leads to the conclusion that each conformal class of every compact surface with a
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Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-01-23
Abstract We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to
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The Statistical Theory of the Angiogenesis Equations J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-01-22 Björn Birnir, Luis Bonilla, Manuel Carretero, Filippo Terragni
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Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process J. Nonlinear Sci. (IF 3.0) Pub Date : 2024-01-02 Qun Liu, Daqing Jiang
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Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-30 Wenjie Hu, Tomás Caraballo
The aim of this paper is to propose a new method to construct pullback exponential attractors with explicit fractal dimensions for non-autonomous infinite-dimensional dynamical systems in Banach spaces. The approach is established by combining the squeezing properties and the covering of finite subspace of Banach spaces, which generalize the method established for autonomous systems in Hilbert spaces
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Geometry-Preserving Numerical Methods for Physical Systems with Finite-Dimensional Lie Algebras J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-23 L. Blanco, F. Jiménez, J. de Lucas, C. Sardón
Abstract We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie group action and then generates the discrete solution of the Lie system on the manifold via a solution of the Lie system on the Lie group. One major result
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Spike Solutions to the Supercritical Fractional Gierer–Meinhardt System J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-18 Daniel Gomez, Markus De Medeiros, Jun-cheng Wei, Wen Yang
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Numerical Computation of Dark Solitons of a Nonlocal Nonlinear Schrödinger Equation J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-18 André de Laire, Guillaume Dujardin, Salvador López-Martínez
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Geometric Methods for Adjoint Systems J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-19 Brian Kha Tran, Melvin Leok
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Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-08 Felix X.-F. Ye, Sichen Yang, Mauro Maggioni
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Error Estimates of hp Spectral Element Methods in Nonlinear Optimal Control Problem J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-12-01 Xiuxiu Lin, Yanping Chen, Yunqing Huang
The main purpose of this paper is to discuss hp spectral element method for optimal control problem governed by a nonlinear elliptic equation with \(L^2\)-norm constraint for control variable. We then set up its weak formulation and hp spectral element approximation scheme. A priori error estimates of hp spectral element approximation based on some suitable projection operators are proved carefully
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Well-Posedness and Stability Analysis of a Landscape Evolution Model J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-24 Julie Binard, Pierre Degond, Pascal Noble
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Oscillations in a Fully Connected Network of Leaky Integrate-and-Fire Neurons with a Poisson Spiking Mechanism J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-17 Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu
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Cognitive Consumer-Resource Spatiotemporal Dynamics with Nonlocal Perception J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-18 Yongli Song, Hao Wang, Jinfeng Wang
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Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-16 S. Jelbart, C. Kuehn, S.-V. Kuntz
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Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-15 Stephan Wojtowytsch
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Phase-Locked Solutions of a Coupled Pair of Nonidentical Oscillators J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-11 Kuan-Wei Chen, Chih-Wen Shih
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Phase-Amplitude Coordinate-Based Neural Networks for Inferring Oscillatory Dynamics J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-11 Talha Ahmed, Dan Wilson
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A Nonlocal Reaction-Diffusion Model of West Nile Virus with Vertical Transmission J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-07 Feng-Bin Wang, Ruiwen Wu, Xiao-Qiang Zhao
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Accurate Computations up to Breakdown of Quasi-Periodic Attractors in the Dissipative Spin–Orbit Problem J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-07 Renato Calleja, Alessandra Celletti, Joan Gimeno, Rafael de la Llave
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Wigner Equations for Phonons Transport and Quantum Heat Flux J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-03 V. D. Camiola, V. Romano, G. Vitanza
Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the acoustic, optical and Z phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal’s calculus and its properties, the pseudo-differential operators are expanded up to the second order in \(\hbar \). An energy transport
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Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-06 Riccardo Durastanti, Lorenzo Giacomelli
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Hamiltonian Mechanics and Lie Algebroid Connections J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-11-02 Jiawei Hu, Ari Stern
We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and vertical dynamics. We show that these dynamics can be obtained in two equivalent ways: (1) using the canonical Lie–Poisson structure, expressed in terms of the connection;
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Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-30 Erhan Bayraktar, Qi Feng, Wuchen Li
We study long-time dynamical behaviors of weakly self-consistent Vlasov–Fokker–Planck equations. We introduce Hessian matrix conditions on mean-field kernel functions, which characterizes the exponential convergence of solutions in \(L^1\) distances. The matrix condition is derived from the dissipation of a selected Lyapunov functional, namely auxiliary Fisher information functional. We verify proposed
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Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-30 Jason J. Bramburger, Giovanni Fantuzzi
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Blowup Analysis of a Hysteresis Model Based Upon Singular Perturbations J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-26 K. U. Kristiansen
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A Hydrodynamical Model of Nematic Liquid Crystal Films with a General State of Orientational Order J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-21 Lucas Bouck, Ricardo H. Nochetto, Vladimir Yushutin
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Pulsating Fronts of Spatially Periodic Bistable Reaction–Diffusion Equations Around an Obstacle J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-17 Fu-Jie Jia, Wei-Jie Sheng, Zhi-Cheng Wang
In this paper, we study a spatially periodic bistable-type reaction–diffusion equation in so-called exterior domains \(\Omega ={\mathbb {R}}^N\backslash K\), where \(K\subset {\mathbb {R}}^N\) is a compact set and denotes an obstacle. For any direction \(e\in {\mathbb {S}}^{N-1}\), if the spatially periodic bistable reaction–diffusion equation in \({\mathbb {R}}^N\) admits a moving pulsating front
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Non-existence of Mean-Field Models for Particle Orientations in Suspensions J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-16 Richard M. Höfer, Amina Mecherbet, Richard Schubert
We consider a suspension of spherical inertialess particles in a Stokes flow on the torus \(\mathbb {T}^3\). The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientation can be valid. This contrasts with widely used models in the literature such as the FENE and Doi
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Incompressible Limit of the Ericksen–Leslie Parabolic–Hyperbolic Liquid Crystal Model J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-14 Liang Guo, Ning Jiang, Fucai Li, Yi-Long Luo, Shaojun Tang
Ericksen and Leslie proposed a hydrodynamic model for liquid crystals in the format of conservation laws in the 1960s. Their original model includes inertial and compressibility effects, which makes the model a coupled parabolic–hyperbolic system. In this paper we build up the connection between the compressible and incompressible parabolic–hyperbolic liquid crystal model in the framework of classical
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Fractional-Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-06 Sachin Bhalekar, Prashant M. Gade
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On the Poincaré–Bendixson Formula for Planar Piecewise Smooth Vector Fields J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-05 Shimin Li, Changjian Liu, Jaume Llibre
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Systematic Search for Singularities in 3D Euler Flows J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-06 Xinyu Zhao, Bartosz Protas
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Rogue Waves and Their Patterns in the Vector Nonlinear Schrödinger Equation J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-04 Guangxiong Zhang, Peng Huang, Bao-Feng Feng, Chengfa Wu
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Response Solutions in Singularly Perturbed, Quasi-Periodically Forced Nonlinear Oscillators J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-04 Wen Si, Lu Xu, Yingfei Yi
For a quasi-periodically forced oscillator, response solutions are quasi-periodic ones having the same frequencies as that of the forcing function. Typically being the most stable or robust ones, they form an important class of oscillatory solutions of the oscillator. Since the introduction of the notion in the 1950 s, response solutions have been extensively studied in regularly perturbed, quasi-periodically
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A Three-Dimensional Generalization of QRT Maps J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-05 Jaume Alonso, Yuri B. Suris, Kangning Wei
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On the Discretely Self-similar Solutions to the Euler Equations in $${\mathbb {R}}^3$$ J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-10-04 Dongho Chae, Jörg Wolf
We remove \((\alpha , \lambda )\)-discretely self-similar blow up for solutions to the Euler equations for \(\alpha \ge \frac{3}{2}\), for which we allow sublinear growth for the profile. More precisely, we show that there are only spatial constant \((\alpha , \lambda )\)-discretely self-similar solutions \(v=c(t)\) having the sublinear growth at the infinity. For the proof, we establish a new a priori
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On a Mathematical Analysis of a Coupled System Adapted to MRI Image Denoising J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-30 A. El Hakoume, Z. Zaabouli, L. Afraites, A. Laghrib
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On the Role of the Displacement Current and the Cattaneo’s Law on Boundary Layers of Plasma J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-27 Nacer Aarach, Francesco De Anna, Marius Paicu, Ning Zhu
In the present paper, we aim to mathematically analyse the role of the displacement current and the Cattaneo’s law on the boundary-layer theory of plasma, when the corresponding characteristic speed is relativistic. We restrict our analysis to two-dimensional flows and we study the asymptotic limit of the Navier–Stokes–Maxwell equations with Cattaneo’s law near a bounding flat line, when the Hartmann
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J-Trajectories in 4-Dimensional Solvable Lie Group $$\textrm{Sol}_1^4$$ J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-25 Zlatko Erjavec, Jun-ichi Inoguchi
J-trajectories are arc-length-parameterized curves in almost Hermitian manifolds, which satisfy the equation \(\nabla _{{\dot{\gamma }}}{\dot{\gamma }}=q J {\dot{\gamma }}\). In this paper, J-trajectories in the solvable Lie group \(\textrm{Sol}_1^4\) are investigated. J-trajectories of osculating order 2 and 3, homogeneous J-trajectories and J-trajectories in subspace\(\textrm{Nil}_3\) are examined
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Data Assimilation Using Time-Delay Nudging in the Presence of Gaussian Noise J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-25 Emine Celik, Eric Olson
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Reconnection of Infinitely Thin Antiparallel Vortices and Coherent Structures J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-22 Sergei Iakunin, Luis Vega
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Maxwell’s Equations in a Plane Waveguide with Nonhomogeneous Nonlinear Permittivity: Analytical and Numerical Approaches J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-19 S. V. Tikhov, D. V. Valovik
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Complex Dynamics of a Stochastic SIR Epidemic Model with Vertical Transmission and Varying Total Population Size J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-21 Xiao-Bing Zhang, Liang Zheng
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Large Amplitude Radially Symmetric Spots and Gaps in a Dryland Ecosystem Model J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-21 Eleanor Byrnes, Paul Carter, Arjen Doelman, Lily Liu
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Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-19 T. Congy, G. A. El, G. Roberti, A. Tovbis
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Well-Posedness of a Nonlinear Shallow Water Model for an Oscillating Water Column with Time-Dependent Air Pressure J. Nonlinear Sci. (IF 3.0) Pub Date : 2023-09-19 Edoardo Bocchi, Jiao He, Gastón Vergara-Hermosilla