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