Investigation of interaction solutions for modified Korteweg-de Vries equation by consistent Riccati expansion method. (English) Zbl 1435.35337

Summary: A consistent Riccati expansion (CRE) method is proposed for obtaining interaction solutions to the modified Korteweg-de Vries (mKdV) equation. Using the CRE method, it is shown that interaction solutions such as the soliton-tangent (or soliton-cotangent) wave cannot be constructed for the mKdV equation. More importantly, exact soliton-cnoidal periodic wave interaction solutions are presented. While soliton-cnoidal interaction solutions were found to degenerate to special resonant soliton solutions for the values of modulus (\(n\)) closer to one (upper bound of modulus) in the Jacobi elliptic function, a normal kink-shaped soliton was observed for values of \(n\) closer to zero (lower bound).


35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35C05 Solutions to PDEs in closed form
Full Text: DOI


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