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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.

MSC:

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