Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations

Wen-Xin Zhang; Yaqing Liu; Wen-Xin Zhang; Yaqing Liu

doi:10.3934/math.2021641

AIMS Mathematics

2021, Volume 6, Issue 10: 11046-11075. doi: 10.3934/math.2021641

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Research article

Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations

Wen-Xin Zhang ,
Yaqing Liu ^,

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received: 22 June 2021 Accepted: 25 July 2021 Published: 30 July 2021
MSC : 35Q51, 37K40

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.
- nonlocal cmKdV equation,
- soliton solutions,
- Hirota bilinear method,
- integrability,
- Lax pair
Citation: Wen-Xin Zhang, Yaqing Liu. Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations[J]. AIMS Mathematics, 2021, 6(10): 11046-11075. doi: 10.3934/math.2021641

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Abstract

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.

References

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