A. Visinescu, D. Grecu, R. Fedele, S. De Nicola, “Madelung fluid description of the generalized derivative nonlinear Schrödinger equation: Special solutions and their stability”, TMF, 2009, Volume 160, Number 1,Pages <nobr>229

This article is cited in 12 papers

Madelung fluid description of the generalized derivative nonlinear Schrödinger equation: Special solutions and their stability

A. Visinescu^a, D. Grecu^a, R. Fedele^b, S. De Nicola^c

^a National Institute for Physics and Nuclear Engineering
^b Università degli Studi di Napoli Federico II
^c Istituto di Cibernetica "Eduardo Caianiello"

Abstract: A correspondence between the families of generalized nonlinear Schrödinger (NLS) equations and generalized KdV equations was recently found using a Madelung fluid description. We similarly consider a special derivative NLS equation. We find a number of solitary waves and periodic solutions (expressed in terms of elliptic Jacobi functions) for a motion with a stationary profile current velocity. We study the stability of a bright solitary wave (ground state) by conjecturing that the Vakhitov–Kolokolov criterion is applicable.

Keywords: nonlinear partial differential equation, generalized nonlinear Schrödinger equation, generalized Korteweg–de Vries equation, Madelung fluid description.

DOI: 10.4213/tmf6394