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New Jacobi elliptic function-like solutions for the general KdV equation with variable coefficients. (English) Zbl 1255.35193
Summary: An improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation is used to construct more new exact solutions of a generalized KdV equation with variable coefficients. As a result, seven families of new generalized Jacobi elliptic function-like solutions, soliton-like solutions and trigonometric function solutions of the equation are obtained by using this method, which shows that the general method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
33E05 Elliptic functions and integrals
35B10 Periodic solutions to PDEs
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