论文标题
分数n-溶解子与可集成的组合分数高阶MKDV层次结构的异常分散体的相互作用
Interactions of fractional N-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy
论文作者
论文摘要
在本文中，我们研究了异常的分散关系，逆散射转换，带有riemann-hilbert（RH）问题，以及可集成的组合组合分数高阶MKDV（FHMKDV）层次的分数多溶剂，包括分数MKDV（FMKDV），FRACTICTION fractional fractional fractional fractional fractiont（FMKD）（f5 f5）。第三阶MKDV（F35MKDV）方程等，可以通过ZS光谱问题的平方标量特征函数的完整性来表征。我们构建了一个矩阵RH问题，以提出三种类型的分数N- soliton，以说明无反射情况的FHMKDV层次结构的异常分散体。作为一些示例，我们分析了分数一soliton的波速度，因此我们发现FHMKDV方程可预测波速度和振幅之间的功率定律关系，并证明异常分散体。此外，我们说明了其他有趣的异常分散波现象，其中包含分数明亮和深色孤子，W形孤子和深色孤子以及呼吸和深色孤子的弹性相互作用。这些获得的分数多solitons将有助于了解分数非线性培养基中相关的非线性超分散波传播。
In this paper, we investigate the anomalous dispersive relations, inverse scattering transform with a Riemann-Hilbert (RH) problem, and fractional multi-solitons of the integrable combined fractional higher-order mKdV (fhmKdV) hierarchy, including the fractional mKdV (fmKdV), fractional fifth-order mKdV (f5mKdV), fractional combined third-fifth-order mKdV (f35mKdV) equations, etc., which can be featured via completeness of squared scalar eigenfunctions of the ZS spectral problem. We construct a matrix RH problem to present three types of fractional N-solitons illustrating anomalous dispersions of the combined fhmKdV hierarchy for the reflectionless case. As some examples, we analyze the wave velocity of the fractional one-soliton such that we find that the fhmKdV equation predicts a power law relationship between the wave velocity and amplitude, and demonstrates the anomalous dispersion. Furthermore, we illustrate other interesting anomalous dispersive wave phenomena containing the elastic interactions of fractional bright and dark solitons, W-shaped soliton and dark soliton, as well as breather and dark soliton. These obtained fractional multi-solitons will be useful to understand the related nonlinear super-dispersive wave propagations in fractional nonlinear media.
