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A new general algebraic method with symbolic computation to construct new doubly-periodic solutions of the \((2 + 1\))-dimensional dispersive long wave equation. (English) Zbl 1082.65577

Summary: For constructing more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations, a new direct and unified algebraic method, named Jacobi elliptic function rational expansion method, is presented and implemented in a computer algebraic system. Compared with most of the existing Jacobi elliptic function expansion methods, the proposed method can be expected to obtain new and more general formal solutions. We choose a (2 + 1)-dimensional dispersive long wave equation to illustrate the method.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L75 Higher-order nonlinear hyperbolic equations
68W30 Symbolic computation and algebraic computation

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