Madelung fluid description of the generalized derivative nonlinear Schrodinger equation: special solutions and their stability

Year: 2009

Authors: Visinescu A., Grecu D., Fedele R., De Nicola S.

Autors Affiliation: Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering “Horia Hulubei,” Bucharest, Romania;
University “Federico II,” Naples, Italy;
Institute of Cybernetics “Eduardo Caianello,” Pozzuoli, Naples, Italy

Abstract: A correspondence between the families of generalized nonlinear Schrodinger (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.

Journal/Review: THEORETICAL AND MATHEMATICAL PHYSICS

Volume: 160 (1)      Pages from: 1066  to: 1074

KeyWords: generalized nonlinear Schr¨odinger equat; Madelung fluid description; Korteweg–de Vries equation,
DOI: 10.1007/s11232-009-0098-z

Citations: 10
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