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Abundant families of new traveling wave solutions for the coupled Drinfel’d-Sokolov-Wilson equation. (English) Zbl 1062.35018

Summary: The generalized Jacobi elliptic function method is further improved by introducing an elliptic function \(\phi(\xi)\) as a new independent variable and it is easy to calculate the over-determined equations. Abundant new traveling wave solutions of the coupled Drinfel’d-Sokolov-Wilson equation are obtained. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions.

MSC:

35C05 Solutions to PDEs in closed form
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35N10 Overdetermined systems of PDEs with variable coefficients
35B10 Periodic solutions to PDEs
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