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Generalized polynomial expansions for finding traveling wave solutions
Carmen Ionescu,Radu Constantinescu
Keywords:Traveling wave solutions, polynomial expansion, auxiliary equations, balancing procedure, KdV equation
Abstract:
      The paper proposes a generalized analytic approach which allows finding traveling wave solutions for some nonlinear PDEs. The solutions are expressed as polynomial expansions of the known solutions of an auxiliary equation. The proposed formalism integrates classical approaches as tanh method or G’/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’/G approach can be recovered now in an unified and very natural way.