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.
Madelung fluid description of generalized derivative NLS equation: special solutions and their stability / A., Visinescu; D., Grecu; Fedele, Renato; S., De Nicola. - In: THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 0040-5779. - STAMPA. - 160:(2009), pp. 1066-1074. [10.1007/s11232-009-0098-z]
Madelung fluid description of generalized derivative NLS equation: special solutions and their stability
FEDELE, RENATO;
2009
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
