Fedele, Renato (2009) Madelung fluid description of generalized derivative NLS equation: special solutions and their stability. [Pubblicazione in rivista scientifica]

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Item Type: Pubblicazione in rivista scientifica
Uncontrolled Keywords: nonlinear partial differential equation, generalized nonlinear Schroedinger equation, generalized Korteweg–de Vries equation, Madelung fluid description
Date Deposited: 21 Oct 2010 06:56
Last Modified: 30 Apr 2014 19:43
URI: http://www.fedoa.unina.it/id/eprint/7446


A correspondence between the families of generalized nonlinear Schr¨odinger (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.

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