A Multidimensional Superposition Principle: Classical Solitons IV

DOI

10.1080/14029251.2018.1440740How to use a DOI?

Keywords

Solitons; Nonlinear interactions; Superposition formulae

Abstract

This article continues the series of the works of 1998–2007 years devoted to the Multidimensional Superposition Principle, the concept easily explaining both classical soliton and more complex wave interactions in nonlinear PDEs and allowing one, in particular, to construct the general Superposition Formulae for nonlinear wave interactions. In the present research the technique of multiexpansions with constraints is considered for finding the above SFs and investigation of the related solitons. (The simplest case of such expansions technically is analogous to the so-called invariant truncated singular expansions.) As the applications, the soliton SFs of the MKdV_±, Kaup-Kupershmidt and new A_± equation are obtained for the bell-shape exponential solitons of the various families, algebraic solitons, and the configuration of the two noninteracting kinks. The linearized, parameterized versions of these SFs are investigated then, and the related analysis of the interactions is presented. The obtained results allow one to consider the one soliton solutions mentioned as the strong bound states of the simpler solitons. Concerning the results for the above concrete nonlinear PDEs, the approach being developed made it possible both to obtain the new results and to reveal new moments for the already known ones.

Copyright

© 2018 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Alexander A. Alexeyev
PY  - 2021
DA  - 2021/01/06
TI  - A Multidimensional Superposition Principle: Classical Solitons IV
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 33
VL  - 25
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1440740
DO  - 10.1080/14029251.2018.1440740
ID  - Alexeyev2021
ER  -