论文标题
分数可集成的非线性孤子方程
Fractional Integrable Nonlinear Soliton Equations
论文作者
论文摘要
非线性积分方程是非线性动力学的基础，而分数方程在异常扩散中众所周知。我们通过介绍发现一类新类的集成分数非线性进化方程来连接这两个字段，这些方程描述了分数介质中的分散运输。这些方程可以使用完整性关系，分散关系和反向散射转换技术的广泛概括的数学过程从非线性集成方程构建。作为示例，该通用方法用于表征两个物理相关的，可普遍的可相关的非线性方程：korteweg-de vries和nonlinearschrödinger方程。这些方程式显示可以预测分数培养基中非分离孤子的超分散运输。
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional nonlinear evolution equations describing dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process utilizing completeness relations, dispersion relations, and inverse scattering transform techniques. As examples, this general method is used to characterize fractional extensions to two physically relevant, pervasive integrable nonlinear equations: the Korteweg-de Vries and nonlinear Schrödinger equations. These equations are shown to predict super-dispersive transport of non-dissipative solitons in fractional media.
