Nonclassical quantum mechanics along with dispersive interactions of free particles, long-range boson stars, hydrodynamics, harmonic oscillator, shallow-water waves, and quantum condensates can be modeled via the nonlinear fractional Schrödinger equation. In this paper, various types of optical soliton wave solutions are investigated for perturbed, conformable space-time fractional Schrödinger model competed with a weakly nonlocal term. The fractional derivatives are described by means of conformable space-time fractional sense. Two different types of nonlinearity are discussed based on Kerr and dual power laws for the proposed fractional complex system. The method employed for solving the nonlinear fractional resonant Schrödinger model is the hyperbolic function method utilizing some fractional complex transformations. Several types of exact analytical solutions are obtained, including bright, dark, singular dual-power-type soliton and singular Kerr-type soliton solutions. More...

中文翻译：

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具有完全非线性项的服从意义上的非线性共振时空Schrödinger方程的孤子解的结构

非经典量子力学以及自由粒子，远程玻色子星，流体力学，谐波振荡器，浅水波和量子凝聚物的色散相互作用可以通过非线性分数薛定ding方程建模。在本文中，研究了各种类型的孤子光解，以解决与弱非局部项竞争的扰动，适度时空分数薛定ding模型。分数导数通过一致的时空分数意义来描述。基于Kerr和对偶幂定律，讨论了所提出的分数复杂系统的两种不同类型的非线性。用于求解非线性分数阶共振Schrödinger模型的方法是利用一些分数阶复数变换的双曲函数方法。得到了几种类型的精确解析解，包括亮，暗，奇异双幂型孤子和奇异Kerr型孤子溶液。更多...