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

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 s...

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Published inAIMS mathematics Vol. 6; no. 10; pp. 11046 - 11075
Main Authors Zhang, Wen-Xin, Liu, Yaqing
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
hirota bilinear method
integrability
lax pair
nonlocal cmkdv equation
soliton solutions
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ISSN2473-6988
2473-6988
DOI10.3934/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.
AbstractList 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.
Author Liu, Yaqing
Zhang, Wen-Xin
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SubjectTerms hirota bilinear method
integrability
lax pair
nonlocal cmkdv equation
soliton solutions
Title Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations
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