Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

doi:10.1088/1674-1056/acae7d

中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50204-050204.doi: 10.1088/1674-1056/acae7d

Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

Hangbing Shao(邵杭兵) and Bilige Sudao(苏道毕力格)^†

Department of Mathemaitc, Inner Mongolia University of Technology, Hohhote 010051, China

收稿日期:2022-10-20 修回日期:2022-12-03 接受日期:2022-12-27 出版日期:2023-04-21 发布日期:2023-05-05
通讯作者: Bilige Sudao E-mail:inmathematica@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12061054) and Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region of China (Grant No. NJYT-20-A06).

Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

Hangbing Shao(邵杭兵) and Bilige Sudao(苏道毕力格)^†

Department of Mathemaitc, Inner Mongolia University of Technology, Hohhote 010051, China

Received:2022-10-20 Revised:2022-12-03 Accepted:2022-12-27 Online:2023-04-21 Published:2023-05-05
Contact: Bilige Sudao E-mail:inmathematica@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12061054) and Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region of China (Grant No. NJYT-20-A06).

摘要/Abstract

摘要： We gave the localized solutions, the interaction solutions and the mixed solutions to a reduced (3+1)-dimensional nonlinear evolution equation. These solutions were characterized by superposition formulas of positive quadratic functions, the exponential and hyperbolic functions. According to the known lump solution in the outset, we obtained the superposition formulas of positive quadratic functions by plausible reasoning. Next, we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory. These two kinds of solutions contained superposition formulas of positive quadratic functions, which were turned into general ternary quadratic functions, the coefficients of which were all rational operation of vector inner product. Then we obtained linear superposition formulas of exponential and hyperbolic function solutions. Finally, for aforementioned various solutions, their dynamic properties were showed by choosing specific values for parameters. From concrete plots, we observed wave characteristics of three kinds of solutions. Especially, we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

关键词: localized solutions, mixed solutions, Hirota bilinear method, linear superposition formulas

Abstract: We gave the localized solutions, the interaction solutions and the mixed solutions to a reduced (3+1)-dimensional nonlinear evolution equation. These solutions were characterized by superposition formulas of positive quadratic functions, the exponential and hyperbolic functions. According to the known lump solution in the outset, we obtained the superposition formulas of positive quadratic functions by plausible reasoning. Next, we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory. These two kinds of solutions contained superposition formulas of positive quadratic functions, which were turned into general ternary quadratic functions, the coefficients of which were all rational operation of vector inner product. Then we obtained linear superposition formulas of exponential and hyperbolic function solutions. Finally, for aforementioned various solutions, their dynamic properties were showed by choosing specific values for parameters. From concrete plots, we observed wave characteristics of three kinds of solutions. Especially, we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

Key words: localized solutions, mixed solutions, Hirota bilinear method, linear superposition formulas

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations)

Hangbing Shao(邵杭兵) and Bilige Sudao(苏道毕力格). Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation[J]. 中国物理B, 2023, 32(5): 50204-050204.

Hangbing Shao(邵杭兵) and Bilige Sudao(苏道毕力格). Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation[J]. Chin. Phys. B, 2023, 32(5): 50204-050204.

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Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

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