THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

doi:10.1007/s10473-021-0520-7

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1733-1748.doi: 10.1007/s10473-021-0520-7

THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

肖羽¹, 徐建², 范恩贵³

1. College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. School of Mathematical Science, Fudan University, Shanghai 200433, China

收稿日期:2019-09-11 修回日期:2021-02-05 出版日期:2021-10-25 发布日期:2021-10-21
通讯作者: Yu XIAO E-mail:yuxiao5726@163.com
作者简介:Jian XU,E-mail:jianxu@usst.edu.cn;Engui FAN,E-mail:faneg@fudan.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (11901167, 11971313 and 51879045), Key scientific research projects of higher education institutions in Henan, China (18B110008).

THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

Yu XIAO¹, Jian XU², Engui FAN³

1. College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. School of Mathematical Science, Fudan University, Shanghai 200433, China

Received:2019-09-11 Revised:2021-02-05 Online:2021-10-25 Published:2021-10-21
Contact: Yu XIAO E-mail:yuxiao5726@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11901167, 11971313 and 51879045), Key scientific research projects of higher education institutions in Henan, China (18B110008).

摘要/Abstract

摘要： In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with $3\times 3$ Lax pair on the finite interval $[0,L]$. The solution can be expressed by the solution of a $3\times 3$ Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions $s(k),S(k),S_{l}(k)$, which are determined by initial data at $t=0$, boundary values at $x=0$ and boundary values at $x=L$, respectively. What's more, since the eigenvalues of $3\times 3$ coefficient matrix of $k$ spectral parameter in Lax pair are three different values, search for the path of analytic functions in RH problem becomes a very interesting thing.

关键词: integral equation, initial boundary value problems, Fokas unified method, Riemann-Hilbert problem

Abstract: In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with $3\times 3$ Lax pair on the finite interval $[0,L]$. The solution can be expressed by the solution of a $3\times 3$ Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions $s(k),S(k),S_{l}(k)$, which are determined by initial data at $t=0$, boundary values at $x=0$ and boundary values at $x=L$, respectively. What's more, since the eigenvalues of $3\times 3$ coefficient matrix of $k$ spectral parameter in Lax pair are three different values, search for the path of analytic functions in RH problem becomes a very interesting thing.

Key words: integral equation, initial boundary value problems, Fokas unified method, Riemann-Hilbert problem

中图分类号:

35Q58

肖羽, 徐建, 范恩贵. THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL[J]. 数学物理学报(英文版), 2021, 41(5): 1733-1748.

Yu XIAO, Jian XU, Engui FAN. THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL[J]. Acta mathematica scientia,Series B, 2021, 41(5): 1733-1748.

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THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

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