Part of Springer Nature

Journal of Nonlinear Mathematical Physics

Volume 27, Issue 3, May 2020, Pages 429 - 452

Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions

Authors
John Cobb*, Alex Kasman, Albert Serna, Monique Sparkman
Department of Mathematics, College of Charleston, Charleston SC 29401
*

Current address: Department of Mathematics, University of Wisconsin, Madison WI 53706

Corresponding Author
Alex Kasman
Received 18 June 2019, Accepted 3 November 2019, Available Online 4 May 2020.
DOI
https://doi.org/10.1080/14029251.2020.1757234How to use a DOI?
Abstract

Quaternion-valued solutions to the non-commutative KdV equation are produced using determinants. The solutions produced in this way are (breather) soliton solutions, rational solutions, spatially periodic solutions and hybrids of these three basic types. A complete characterization of the parameters that lead to non-singular 1-soliton and periodic solutions is given. Surprisingly, it is shown that such solutions are never singular when the solution is essentially non-commutative. When a 1-soliton solution is combined with another solution through an iterated Darboux transformation, the result behaves asymptotically like a combination of different solutions. This “non-linear superposition principle” is used to find a formula for the phase shift in the general 2-soliton interaction. A concluding section compares these results with other research on non-commutative soliton equations and lists some open questions.

Copyright
© 2020 The Authors. Published by Atlantis 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
27 - 3
Pages
429 - 452
Publication Date
2020/05
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1757234How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis 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  - John Cobb
AU  - Alex Kasman
AU  - Albert Serna
AU  - Monique Sparkman
PY  - 2020
DA  - 2020/05
TI  - Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 429
EP  - 452
VL  - 27
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1757234
DO  - https://doi.org/10.1080/14029251.2020.1757234
ID  - Cobb2020
ER  -