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

Socpus ID

74249094937 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/74249094937

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