On the N-Wave Equations and Soliton Interactions in Two and Three Dimensions

Authors

Vladimir S. Gerdjikov, Bulgarian Academy of Sciences,Follow
Rossen Ivanov, Technological University DublinFollow
Assen V. Kyuldjiev, Bulgarian Academy of SciencesFollow

Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Applied mathematics

Publication Details

Wave Motion

Abstract

Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave _{equations with} Z₂xZ₂ reduction group allow breather-like solitons. Finally it is demonstrated that RHP with sewing function depending on three variables t, x and y provides some special solutions of the N-wave equations in three dimensions.

DOI

http://doi.org10.21427/pbt8-5p79

Recommended Citation

V. Gerdjikov, R. Ivanov and A. Kyuldjiev, On the N-wave equations and soliton interactions in two and three dimensions, Wave Motion, 48 (2011) 791-804. Available from the publisher here http://www.sciencedirect.com/science/journal/01652125/48 doi: 10.21427/pbt8-5p79

Funder

Science Foundation Ireland(Grant No. 09/RFP/MTH2144)