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New Jacobi elliptic functions solutions for the combined KdV-MKdV equation. (English) Zbl 1235.35248
Summary: We establish exact solutions for the combined KdV-MKdV equation. By constructing four new types of Jacobi elliptic functions solutions, the Jacobi elliptic function expansion method is extend. With the aid of symbolic computation system Mathematica we obtain some new exact periodic solutions of the nonlinear combined KdV-MKdV equation. These solutions are degenerated to solitary wave solutions and triangle function solutions in the limit case when the modulus of the Jacobi elliptic functions m1 or m0.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
68W30Symbolic computation and algebraic computation
35B10Periodic solutions of PDE
Software:
Mathematica