Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5508
Title: Envelope soliton resonances and broer-kaup-type non-madelung fluids
Authors: Pashaev, Oktay
Keywords: Broer-Kaup system
Madelung fluid
Envelope soliton
Soliton resonance
Resonant NLS
Issue Date: Aug-2012
Publisher: Pleiades Publishing
Source: Pashaev, O. (2012). Envelope soliton resonances and broer-kaup-type non-madelung fluids. Theoretical and Mathematical Physics, 172(2), 1147-1159. doi:10.1007/s11232-012-0103-9
Abstract: We derive an extended nonlinear dispersion for envelope soliton equations and also find generalized equations of the nonlinear Schrödinger (NLS) type associated with this dispersion. We show that space dilatations imply hyperbolic rotation of the pair of dual equations, the NLS and resonant NLS (RNLS) equations. For the RNLS equation, in addition to the Madelung fluid representation, we find an alternative non-Madelung fluid system in the form of a Broer-Kaup system. Using the bilinear form for the RNLS equation, we construct the soliton resonances for the Broer-Kaup system and find the corresponding integrals of motion and existence conditions for the soliton resonance and also a geometric interpretation in terms of a pseudo-Riemannian surface of constant curvature. This approach can be extended to construct a resonance version and the corresponding Broer-Kaup-type representation for any envelope soliton equation. As an example, we derive a new modified Broer-Kaup system from the modified NLS equation.
URI: http://dx.doi.org/10.1007/s11232-012-0103-9
http://hdl.handle.net/11147/5508
ISSN: 0040-5779
1573-9333
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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