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Zbl 1252.65112
Aslan, Ịsmail
The discrete $(G^{\prime}/G)$-expansion method applied to the differential-difference Burgers equation and the relativistic Toda lattice system. (English)
[J] Numer. Methods Partial Differ. Equations 28, No. 1, 127-137 (2012). ISSN 0749-159X; ISSN 1098-2426/e

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 2000:: *65L03
34K28 Numerical approximation of solutions of FDE
34K13 Periodic solutions of functional differential equations

Keywords: differential-difference Burgers equation; (G$^{\prime}$/G)-expansion method; relativistic Toda lattice system; solitary solutions; periodic solutions; rational solutions

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