非均匀弹性梁介质中的怪波

Rogue Waves in the Non-Uniform Elastic Beam Medium

摘要: 本文以非线性偏微分方程的理论为基础，对非均匀弹性梁介质中的模型——变系数混合非线性薛定谔方程的几种非线性波进行了详细研究。首先根据方程的Lax对构建出了方程的一阶及N阶达布变换。利用构建的达布变换，以零解为种子解求得了变系数混合非线性薛定谔方程的一、二阶孤子解；选取平面波解为种子解，得到了一、二阶呼吸子解和一、二、三阶怪波解。此外，利用符号计算软件，在不同的系数下，对所求得的方程的各种非线性波解进行作图分析，直观地描绘了它们的动力学性质。

Abstract: Based on the theory of nonlinear partial differential equations, several nonlinear waves in the me-dium of inhomogeneous elastic beams, i.e., variable coefficient mixed nonlinear Schrödinger equa-tions, are studied in detail. Firstly, according to the Lax pair of the equations, the 1-order and N-order Darboux transformation of the equation are constructed. By the constructed Darboux transformation, the 1- and 2-order soliton solutions of the variable coefficient mixed nonlinear Schrödinger equation are obtained by using the zero solution as the seed solution; the plane wave solution is selected as the seed solution, and the 1- and 2-order breather solutions and the 1-, 2-, and 3-order rouge wave solutions are obtained. In addition, the symbolic calculation software is used to graph and analyze the various nonlinear wave solutions of the obtained equations under different coefficients, and their dynamic properties are intuitively depicted.