Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations
Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations
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DOI：
10.3934/math.2021641
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发表时间：
2021
期刊：
影响因子：
2.2
通讯作者：
Wen-Xin Zhang;Yaqing Liu
中科院分区：
文献类型：
--
作者：
Wen-Xin Zhang;Yaqing Liu
本文构造了逆空间cmKdV方程、逆时间cmKdV方程和逆时空cmKdV方程，并基于Hirota双线性方法分别推导了三种不同的孤子解。利用变量变换，从局部方程出发，研究了三类非局部方程的Lax可积性。基于三类非局域cmKdV方程的单孤子解和双孤子解的精确解公式，用图形来描述孤子解。根据动力学行为可以发现，这些解具有不同于经典cmKdV方程的新性质。
In this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is studied from local equation by using variable transformations. Based on exact solution formulae of one- and two-soliton solutions of three types of nonlocal cmKdV equation, some figures are used to describe the soliton solutions. According to the dynamical behaviors, it can be found that these solutions possess novel properties which are different from the ones of classical cmKdV equation.