FUNCTIONAL EXPANSIONS FOR FINDING TRAVELING WAVE SOLUTIONS | Zendy

Carmen Ionescu | Zendy; Radu Constantinescu | Zendy; Mihail Stoicescu | Zendy

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FUNCTIONAL EXPANSIONS FOR FINDING TRAVELING WAVE SOLUTIONS

Author(s) -

Carmen Ionescu,

Radu Constantinescu,

Mihail Stoicescu

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20180314

Subject(s) - korteweg–de vries equation , traveling wave , mathematics , formalism (music) , nonlinear system , prime (order theory) , mathematical analysis , physics , combinatorics , art , musical , quantum mechanics , visual arts

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′/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 and extended, in an unified and very natural way.

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