Single soliton of double kinks of the mKdV equation and its stability. (Chinese. English summary) Zbl 1240.35484

Summary: Based on the idea of the hyperbola function expansion method, some analytical solutions of the modified Korteweg-de Vries (mKdV) equation are obtained by introducing new expansion functions. One of the single soliton solutions has a kink-antikink structure and it reduces to a kink-like solution and bell-like solution under different limitations. The stability of the single soliton solution with double kinks is investigated numerically. The results indicate that the soliton is stable under different disturbances.


35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35B35 Stability in context of PDEs