MKdV-KP-Nonlinearity_RDan.pdf (432.4 kB)
Reduction to modified KdV and its KP-like generalization via phase modulation
journal contribution
posted on 2018-11-12, 11:57 authored by Daniel Ratliff, Thomas J. BridgesThe main observation of this paper is that the modified Korteweg–de Vries equation has its natural origin in phase modulation of a basic state such as a periodic travelling wave, or more generally, a family of relative equilibria. Extension to 2 + 1 suggests that a modified Kadomtsev–Petviashvili (or a Konopelchenko–Dubrovsky) equation should emerge, but our result shows that there is an additional term which has gone heretofore unnoticed. Thus, through the novel application of phase modulation a new equation appears as the 2 + 1 extension to a previously known one. To demonstrate the theory it is applied to the cubic-quintic nonlinear Schrödinger (CQNLS) equation, showing that there are relevant parameter values where a modified KP equation bifurcates from periodic travelling wave solutions of the 2 + 1 CQNLS equation.
Funding
The first author was funded by an EPSRC PhD studentship with grant number EP/L505092/1.
History
School
- Science
Department
- Mathematical Sciences
Published in
NonlinearityVolume
31Issue
8Pages
3794 - 3813Citation
RATLIFF, D.J. and BRIDGES, T.J., 2018. Reduction to modified KdV and its KP-like generalization via phase modulation. Nonlinearity, 31 (8), pp.3794-3813.Publisher
© IOP Publishing Ltd & London Mathematical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported (CC BY-NC-ND 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by-nc-nd/3.0/Acceptance date
2017-04-20Publication date
2018Notes
This is a peer-reviewed, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/aabfab.ISSN
0951-7715eISSN
1361-6544Publisher version
Language
- en