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Generalized extended tanh-function method and its application. (English) Zbl 1088.35534

Summary: A new generalized extended tanh-function method is presented for constructing soliton-like, periodic solutions of nonlinear evolution equations (NEEs). Compared with most of the existing tanh-function method, extended tanh-function method, modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By using this method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEEs. We study the (3 + 1)-dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, periodic solutions.

MSC:

35Q51 Soliton equations
35B10 Periodic solutions to PDEs
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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