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Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations. (English) Zbl 1196.68324

Summary: A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Through discussion and example, parallels are drawn to the tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation issues, scope, and limitations of the software are addressed.

MSC:

68W30 Symbolic computation and algebraic computation
35Lxx Hyperbolic equations and hyperbolic systems
39Axx Difference equations
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