Jacobian elliptic function method for nonlinear differential-difference equations. (English) Zbl 1091.34538

Summary: An algorithm is devised to derive exact travelling wave solutions of differential-difference equations by means of Jacobian elliptic function. For illustration, we apply this method to solve the discrete nonlinear Schrödinger equation, the discretized mKdV lattice equation and the hybrid lattice equation. Some explicit and exact travelling wave solutions, such as Jacobian doubly periodic solutions, kink-type solitary wave solutions, are constructed.


34K05 General theory of functional-differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
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