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Simple equations method (SEsM) and its particular cases: Hirota method

Authors: Nikolay K. Vitanov; Zlatinka I. Dimitrova;

Simple equations method (SEsM) and its particular cases: Hirota method

Abstract

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations. We show that the Hirota method is particular case of SEsM for specific form of the function from the Step. 2 of SEsM and for simple equations from the kind of differential equation for exponential function. We illustrate the methodology by obtaining the three-soliton solution of the Korteweg - de Vries equation, two soliton solution of the nonlinear Schrodinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials.

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Powered by OpenAIRE graph
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
27
Top 10%
Average
Top 10%
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