Title
Exact X-Wave Solutions Of The Hyperbolic Nonlinear Schrödinger Equation With A Supporting Potential
Abstract
We find exact solutions of the two- and three-dimensional nonlinear Schrödinger equation with a supporting potential. We focus in the case where the diffraction operator is of the hyperbolic type and both the potential and the solution have the form of an X-wave. Following similar arguments, several additional families of exact solutions can also can be found irrespectively of the type of the diffraction operator (hyperbolic or elliptic) or the dimensionality of the problem. In particular we present two such examples: The one-dimensional nonlinear Schrödinger equation with a stationary and a "breathing" potential and the two-dimensional nonlinear Schrödinger with a Bessel potential. © 2009 Elsevier B.V. All rights reserved.
Publication Date
10-26-2009
Publication Title
Physics Letters, Section A: General, Atomic and Solid State Physics
Volume
373
Issue
44
Number of Pages
4073-4076
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.physleta.2009.09.008
Copyright Status
Unknown
Socpus ID
74249094937 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/74249094937
STARS Citation
Efremidis, Nikolaos K.; Siviloglou, Georgios A.; and Christodoulides, Demetrios N., "Exact X-Wave Solutions Of The Hyperbolic Nonlinear Schrödinger Equation With A Supporting Potential" (2009). Scopus Export 2000s. 11189.
https://stars.library.ucf.edu/scopus2000/11189