A new spectral problem and the related integrable nonlinear evolution equations

Xiao Yang; Dianlou Du

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A new spectral problem and the related integrable nonlinear evolution equations

机译：一种新的光谱问题和相关的可加工非线性演化方程

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Abstract

A new spectral problem is introduced, which is indicated to be the negative counterpart of the mKdV spectral problem. Based on the fact, some integrable nonlinear evolution equations are obtained, including the derivative Schwarzian KdV equation, the mKdV5 equation and the sine–Gordon equation. Besides, Lax pairs and finite genus solutions of the equations are given.

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机译：<！[cdata [ Abstract

介绍了新的频谱问题，这被指示为MKDV光谱问题的负对应。基于该事实，获得了一些可排现的非线性演化方程，包括衍生施瓦珠KDV方程，MKDV5方程和正弦戈登方程。此外，给出了方程的lex对和有限的属性溶液。 ]]>

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来源
《Applied mathematics letters》 |2018年第2018期|共7页
作者
Xiao Yang; Dianlou Du;
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作者单位

School of Mathematics and Statistics Zhengzhou University;

School of Mathematics and Statistics Zhengzhou University;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Spectral problem; Integrable nonlinear evolution equation; Lax pair; Finite genus solution;

机译：光谱问题;可集体非线性演化方程;罗克对;有限的属溶液;

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专利

1. A new spectral problem and the related integrable nonlinear evolution equations [J] . Xiao Yang, Dianlou Du Applied mathematics letters . 2018,第期

机译：一种新的光谱问题和相关的可加工非线性演化方程
2. Comment on "Painleve integrability of two sets of nonlinear evolution equations with nonlinear dispersions" [Phys. Lett. A 262 (1999) 344] [J] . Marinakis V. Physics Letters, A . 2015,第12a13期

机译：评论“两套带有非线性弥散的非线性发展方程的Painleve可积性”。来吧A 262（1999）344]
3. Painleve integrability of two sets of nonlinear evolution equations with nonlinear dispersions [J] . Sen-yue Lou, Qi-xian Wu Physics Letters, A . 1999,第4a5期

机译：两组具有非线性弥散的非线性发展方程的Painleve可积性
4. Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators [C] . Winfried Auzinger, Harald Hofstaetter, Othmar Koch International workshop on computer algebra in scientific computing . 2016

机译：非线性发展方程流的符号操纵及其在分步时间积分器分析中的应用
5. Fourier-Galerkin spectral method for localized solutions of nonlinear equations. [D] . Christou, Marios Andreas. 2003

机译：非线性方程局部解的傅里叶-加勒金谱方法。
6. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations [O] . S. S. Motsa, V. M. Magagula, P. Sibanda -1

机译：非线性发展抛物型方程的二元Chebyshev谱配置拟线性化方法。
7. General structure of nonlinear evolution equations in 1+2 dimensions integrable by the two-dimensional Gelfand-Dickey-Zakharov-Shabat spectral problem and their transformation properties [O] . B. G. Konopelchenko 1983

机译：二维格尔夫兰德 - Zakharov-Shabat谱问题的1 + 2维度非线性演化方程的一般结构及其转化特性
8. New Set of Symmetries of the Integrable Equations, Lie Algebra and Non-Isospectral Evolution Equations-II: (AKNS System) [R] . Li Yishen, Zhu Guocheng 1985

机译：可积方程的新对称，李代数和非等谱发展方程-II :( aKNs系统）

A new spectral problem and the related integrable nonlinear evolution equations

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