## 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).

### MSC:

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

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