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The discrete \((G^{\prime}/G)\)-expansion method applied to the differential-difference Burgers equation and the relativistic Toda lattice system. (English) Zbl 1252.65112

Summary: We introduce the discrete \((G^{\prime}/G)\)-expansion method for solving nonlinear differential-difference equations (NDDEs). As illustrative examples, we consider the differential-difference Burgers equation and the relativistic Toda lattice system. Discrete solitary, periodic, and rational solutions are obtained in a concise manner. The method is also applicable to other types of NDDEs.

MSC:

65L03 Numerical methods for functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K13 Periodic solutions to functional-differential equations
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