CRE Solvability, Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation

This paper is concerned with the fifth-order modified Korteweg-de Vries(fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion(CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion(CTE) method, the nonlocal symmetry related to the consistent tanh expansion(CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlev′e method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed.

This paper is concerned with the fifth-order modified Korteweg-de Vries （fmKdV） equation. It is proved that the fmKdV equation is consistent Riccati expansion （CRE） solvable. Three special form of soliton-cnoidal wave interaction solutions axe discussed analyticM1y and shown graphically. Fhrthermore, based on the consistent tanh ex- pansion （CTE） method, the nonlocM symmetry related to the consistent tanh expansion （CTE） is investigated, we also give the relationship between this kind of nonlocal symmetry and the residuM symmetry which can be obtained with the truncated Painlevg method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlaxged system and the corresponding finite transformation group is computed.