(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
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。
Abstract: 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.
文章引用：黄春. (2 + 1)维空时分数阶Ablowitz-Kaup-Newell-Segur方程的新精确解的构建[J]. 理论数学, 2024, 14(10): 74-80. https://doi.org/10.12677/pm.2024.1410346

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