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Soliton solution classification in the generalized Korteweg–de Vries equation

Nonlinear Dynamics. 2025. No. 113. P. 32641–32648.
Melnikov I.

All possible soliton solutions classification in the generalized KdV equation is given. It is proved that a solitonic solution can be one of four possible types: classical soliton (that is, sign-constant, with one extremum and two inflection points), pyramidal soliton (with a large number of inflection points), classical kink (a monotonic solution that goes to a constant other than zero at plus (minus) infinity with one inflection point) and pyramidal kink (like the classic one, but with a lot of inflection points). The conditions for the various types solitons appearance for certain equations classes with nonlinearity such as a generalized polynomial or the Tchebycheff system of smooth functions are clarified. Examples of equations with a nontrivial soliton form are given.

Research target: Mathematics Physics
Language: English
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Keywords: солитоныsolitonsKorteweg–de Vries equationУравнение Кортевега—де Фриза
Publication based on the results of:
Differential-geometric properties of dynamical systems and mathematical modeling of processes (2025)
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