A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

Gangwei Wang; Kaitong Yang; Haicheng Gu; Fei Guan; A.H. Kara

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A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

机译：一个（2 + 1） - 具有对称和扭结波解决方案的二维正弦 - 戈登和Sinh-Gordon方程

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In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and traveling wave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived.

机译：在本文中，来自众所周知的AKNS系统的（2 + 1）-Dimensional Sine-Gordon方程和Sinh-Gordon方程。基于Hirota Bilinear方法和Lie对称性分析，构建了（2 + 1）-dimensione正弦戈登方程的扭转波解和行波解决方案。（2 + 1）-dimensional Sinh-Gordon方程的行进波解也可以以类似的方式提供。同时，得出保护法。

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《Nuclear physics, B》 |2020年第1期|共14页
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Gangwei Wang; Kaitong Yang; Haicheng Gu; Fei Guan; A.H. Kara;
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1. A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions [J] . Wang Gangwei, Yang Kaitong, Gu Haicheng, Nuclear physics, B . 2020,第1期

机译：一个（2 + 1） - 具有对称和扭结波解决方案的二维正弦 - 戈登和Sinh-Gordon方程
2. Bifurcations of Traveling Wave Solutions for a New (2+1)-Dimensional sine-Gordon and sinh-gordon equations [J] . Minzhi Weil, Shuxia Li Pacific journal of applied mathematics . 2016,第4期

机译：新（2 + 1） - 二维正弦和Sinh-Gordon方程的行进波解决方案的分叉解决方案
3. New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation [J] . Li ZT Applied mathematics and computation . 2010,第11期

机译：（2 + 1）维Sine-Gordon方程的新扭结形解和周期波解
4. On the Numerical Solution of the Sine-Gordon Equation in 2+1 Dimensions [C] . A. G. Bratsos Advances in Computational Methods in Sciences and Engineering 2005 vol.4A; Lecture Series on Computer and Computational Sciences; vol.4A . 2005

机译：关于2 + 1维Sine-Gordon方程的数值解
5. New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions [D] . Tanguay, Allison J. 2012

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7. Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations [O] . Younis Muhammad, Ali Safdar 2015

机译：孤波和冲击波解（1 + 1） - 维扰动克莱因戈登，（1 + 1）维 Kaup-Keperschmidt和（2 + 1）维 ZK-BBm方程

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

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