带强迫项的变系数耦合修正mKdV方程组的新解*

量子电子学报

带强迫项的变系数耦合修正mKdV方程组的新解*

套格图桑†

内蒙古师范大学数学科学学院, 呼和浩特, 010022

出版日期:2019-05-28 发布日期:2019-05-14
作者简介:套格图桑(1964-),蒙古族，内蒙古自治区通辽市人，博士,教授,研究方向:孤立子与可积系统理论及其应用.E-mail: tgts@imnu.edu.cn
基金资助:
* Project supported by the Natural Science Foundation of China(国家自然科学基金,11361040)，the Natural Science Foundation of Inner Mongolia Autonomous Region， China(内蒙古自治区自然科学基金，2015MS0128) and Science Research Foundation of Inner Mongolia National University， China(内蒙古民族大学科学研究基金项目，NMDGP1713)

The new solutions of the variable coefficients coupling correction mKdV equations with forced items*

Taogetusang†

The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022

Published:2019-05-28 Online:2019-05-14

摘要/Abstract

摘要： 通过两个步骤，构造带强迫项的变系数耦合修正 modified Korteweg-de Vries (VCmKdV) 方程组的复合型新解，并分析了解的相互作用。步骤一、给出一种非线性常微分方程的几种新解。步骤二、采用函数变换与一种非线性常微分方程相结合的方法，构造了带强迫项的VCmKdV方程组的由指数函数、三角函数和有理函数组合的复合型新解。这里包括孤子解与周期解复合的解、双孤子解和双周期解。

关键词: 带强迫项的VCmKdV方程组, 函数变换, 复合型新解

Abstract: By two steps, construct the new complexion solutions of the variable coefficients coupling correction modified Korteweg-de Vries (VCmKdV) equations with forced items, and analysis the interaction with the solutions. Step 1, put forward some kinds of new solutions of a kind of the nonlinear ordinary differential equation. Step 2, the method combing the function transformation with a kind of nonlinear ordinary differential equation is put forward, and the new complexion solutions consisting of exponential functions, trigonometric functions and rational functions of the VCmKdV equation with forced items are constructed. These solutions conclude the complexion solutions composed of the soliton solutions and the period solutions, the two soliton solutions and the two period solutions.

套格图桑?. 带强迫项的变系数耦合修正mKdV方程组的新解*[J]. 量子电子学报.

Taogetusang?. The new solutions of the variable coefficients coupling correction mKdV equations with forced items*[J]. Chinese Journal of Quantum Electronics.

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