Journal of Nonlinear Mathematical Physics

Volume 25, Issue 1, February 2018, Pages 1 - 33

A Multidimensional Superposition Principle: Classical Solitons IV

Authors
Alexander A. Alexeyev
Department of Mathematic, Institute for Cybernetics, Moscow Technological University, 78 Vernadskogo Avenue, Moscow 117454, Russian Federation, aalexeyev@mtu-net.ru
Received 8 January 2017, Accepted 14 July 2017, Available Online 6 January 2021.
DOI
https://doi.org/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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 1
Pages
1 - 33
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2018.1440740How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Alexander A. Alexeyev
PY  - 2021
DA  - 2021/01
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  - https://doi.org/10.1080/14029251.2018.1440740
ID  - Alexeyev2021
ER  -