The existence and properties of envelope solitary waves on a periodic traveling-wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed-point computational scheme, a space-time boundary-value problem for bright traveling breather solutions is solved for the weakly nonlinear Benjamin-Bona-Mahony equation, a nonlocal, regularized shallow water wave model, and the strongly nonlinear conduit equation, a nonlocal model of viscous core-annular flows. Curves of unit-mean traveling breather solutions within a three-dimensional parameter space are obtained. Resonance due to nonconvex, rational linear dispersion leads to a nonzero oscillatory background upon which traveling breathers propagate. These solutions exhibit a topological phase jump and so act as defects within the periodic background. For small amplitudes, traveling breathers are well approximated by bright soliton solutions of the nonlinear Schrödinger equation with a negligibly small periodic background. These solutions are numerically continued into the large-amplitude regime as elevation defects on cnoidal or cnoidal-like periodic traveling-wave backgrounds. This study of bright traveling breathers provides insight into systems with nonconvex, nonlocal dispersion that occur in a variety of media such as internal oceanic waves subject to rotation and short, intense optical pulses.

中文翻译：

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具有远距离非凸色散的介质中的明亮移动呼吸器

在典型的非局域色散介质中，对周期性行波背景上的包络孤立波（称为行进呼吸器）的存在和特性进行了数值研究。使用定点计算方案，针对弱非线性 Benjamin-Bona-Mahony 方程、非局部正则化浅水波模型和强非线性管道方程，求解明亮移动呼吸器解的时空边值问题，粘性核心环流的非局部模型。获得了三维参数空间内单位均值移动呼吸器解的曲线。由于非凸、有理线性色散而产生的共振会导致非零振荡背景，移动呼吸器在该背景上传播。这些解决方案表现出拓扑相跳，因此在周期性背景中充当缺陷。对于小振幅，行进呼吸可以通过具有可忽略不计的小周期性背景的非线性薛定谔方程的明亮孤子解来很好地近似。这些解在数值上连续进入大振幅区域，作为椭圆曲线或类椭圆曲线周期性行波背景上的高程缺陷。这项对明亮移动呼吸器的研究提供了对非凸、非局部色散系统的深入了解，这些色散发生在各种介质中，例如受旋转影响的内部海洋波和短而强的光脉冲。