Investigation of interaction solutions for modified Korteweg-de Vries equation by consistent Riccati expansion method (Q2298996)

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).