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Volume 10, Number 2, 2020, Pages 569-583                                                                DOI:10.11948/20180314
Functional expansions for finding traveling wave solutions
Carmen Ionescu,Radu Constantinescu,Mihail Stoicescu
Keywords:Traveling wave solutions, functional expansion, auxiliary equations, balancing procedure, KdV equation.
      The paper proposes a generalized analytic approach which allows to find traveling wave solutions for some nonlinear PDEs. The solutions are expressed as functional expansions of the known solutions of an auxiliary equation. The proposed formalism integrates classical approaches as tanh method or $G^{\prime }/G$ method, but it open the possibility of generating more complex solutions. A general class of second order PDEs is analyzed from the perspective of this formalism, and clear rules related to the balancing procedure are formulated. The KdV equation is used as a toy model to prove how the results obtained before through the $G^{\prime }/G$ approach can be recovered and extended, in an unified and very natural way.
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