(2 + 1)维空时分数阶Ablowitz-Kaup-Newell-Segur方程的新精确解的构建  

Construction of the New Exact Solutions for the Space-Time Fractional (2 + 1)-Dimensional Ablowitz-Kaup-Newell-Segur Equation

作　　者：黄春[1] 

机构地区：[1]四川职业技术学院教师教育学院,四川 遂宁

出　　处：《理论数学》2024年第10期74-80,共7页Pure Mathematics

摘　　要：非线性Ablowitz-Kaup-Newell-Segur方程是一类应用广泛的非线性偏微分方程。(2 + 1)维空时分数阶Ablowitz-Kaup-Newell-Segur方程常用于描述孤立波在光纤中传播的物理过程,本文利用复行波变换和扩展的Tanh-函数展开法,获得了(2 + 1)维空时分数阶Ablowitz-Kaup-Newell-Segur方程的系列新的精确行波解。The Ablowitz-Kaup-Newell-Segur (AKNS) equations, a class of nonlinear partial differential equations, find their utility in a wide array of applications. The space-time fractional (2 + 1)-dimensional AKNS equation, in particular, is capable of describing the physical process of solitary wave propagation in optical fibers. A new class of exact traveling wave solutions of (2 + 1)-dimensional generalized fractional AKNS equation are obtained by employing complex traveling wave transformation and extended Tanh expansion method.

关 键 词：(2 + 1)维分数阶Ablowitz-Kaup-Newell-Segur方程 Riemann-Liouville分数阶导数 精确行波解 Tanh-函数展开法 

分 类 号：O17[理学—数学]