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New rational formal solutions for \((1 + 1)\)-dimensional Toda equation and another Toda equation. (English) Zbl 1142.37370

Summary: We present a new rational expansion method to uniformly construct a series of exact solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some well-known solutions, but also finds some new and general solutions. The efficiency of the method can be demonstrated on \((1 + 1)\)-dimensional Toda equation and another Toda equation.

MSC:

37K60 Lattice dynamics; integrable lattice equations
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