（2+1）维可积非局部非线性Schrödinger方程的n周期波解

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-02-26 DOI:10.1016/j.wavemoti.2025.103526

Zhonglong Zhao, Yu Wang

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引用次数: 0

摘要

本文首次利用数值算法研究了基于宇称-时间对称的（2+1）维可积非局部非线性Schrödinger方程的拟周期波解。利用Hirota的双线性方法和Riemann-theta函数，构造拟周期波解的方程组可以看作是一个非线性过定系统。该系统可转化为非线性最小二乘问题，利用高斯-牛顿算法求解。研究了小振幅极限下单周期波的渐近性质。此外，利用特征线分析了准周期波的动力学行为。构造拟周期波解的方法可进一步推广到其他非局部可积方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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N-periodic wave solutions of the (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations

In this paper, the quasi-periodic wave solutions for the (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations based on parity-time

(P T)

symmetry are investigated through numerical algorithm for the first time. By using the Hirota’s bilinear method and the Riemann-theta function, the system of equations for constructing quasi-periodic wave solutions can be viewed as a nonlinear over-determined system. This system can be transformed into a nonlinear least square problem and solved with the aid of the Gauss–Newton algorithm. The asymptotic property of the one-periodic wave under the small amplitude limit is investigated. Furthermore, the dynamical behaviors of the quasi-periodic waves are analyzed by means of the characteristic lines. The method for constructing the quasi-periodic wave solutions can be further extended into other nonlocal integrable equations.

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.