非局部 KP -型方程的广义双线性导数

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 143-158.

非局部 KP -型方程的广义双线性导数

赵倩^1,^*(),闫璐²()

¹宁波大学科学技术学院浙江宁波 315211
²西京学院计算机学院西安 710123

收稿日期:2022-01-06 修回日期:2022-07-22 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*赵倩, E-mail: zhaoqian1@nbu.edu.cn
作者简介:闫璐, E-mail: 20190144@xijing.edu.cn
基金资助:
国家自然科学基金(11971251);陕西省教育厅科研计划项目(18JK0987)

Nonlocal KP-type Equations with Generalized Bilinear Derivative

Zhao Qian^1,^*(),Yan Lu²()

¹College of Science & Technology Ningbo University, Zhejiang Ningbo 315211
²School of Computer Science, Xijing University, Xi'an 710123

Received:2022-01-06 Revised:2022-07-22 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(11971251);Scientific Research Program Funded by Shaanxi Provincial Education Department(18JK0987)

摘要/Abstract

摘要：

将 Hirota 双线性方法进行推广, 得到广义的双线性变换方法, 并应用于研究具有非局部项的非线性色散方程. 该文利用本方法研究了包括 KPII, BKP 和 (3+1) -维 gKP 的 KP -型方程, 导出了它们的非局部形式, 作为结论, 借助性质构造了 KP -型方程的孤立波解和近似解.

关键词: 双线性变换方法, 广义双线性导数, 近似解, KP 方程, BKP 方程

Abstract:

A generalized bilinear transformation method, as an extension of bilinear transformation method due to Hirota, is applied to study the nonlinear dispersive equations with nonlocal terms. With this method, the KP-type equations including the KP-II, BKP and (3+1)-dimensional generalized KP equations are studied and their nonlocal forms are derived. As the conclusions, the solitary wave solutions and approximate solutions of those KP-type equations are constructed by developing the bilinear transformation method.

Key words: Bilinear transform method, Generalized bilinear derivative, Approximate solution, KP equation, BKP equation

中图分类号:

O175.2

赵倩, 闫璐. 非局部 KP -型方程的广义双线性导数[J]. 数学物理学报, 2023, 43(1): 143-158.

Zhao Qian, Yan Lu. Nonlocal KP-type Equations with Generalized Bilinear Derivative[J]. Acta mathematica scientia,Series A, 2023, 43(1): 143-158.

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