Non-existence and existence of localized solitary waves for the two-dimensional long-wave-short-wave interaction equations

DOI10.1016/J.AML.2009.10.010zbMath1188.35040OpenAlexW2082016968MaRDI QIDQ963810

B. E. Eshmatov

Publication date: 14 April 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2009.10.010

zbMATH Keywords

Pohozaev-type identitiesexistence of solitary waveslong-wave-short-wave interaction equationsnon-existence of solitary waves

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Soliton solutions (35C08) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Related Items (1)

Transverse linear instability of solitary waves for coupled long-wave-short-wave interaction equations

Cites Work

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• Long-wave short-wave resonance for nonlinear geometric optics.
• Standing waves for a generalized Davey–Stewartson system
• On the existence of standing waves for a davey–stewartson system
• On two-dimensional packets of capillary-gravity waves
• Some solutions pertaining to the resonant interaction of long and short waves
• On a nonlinear Schrödinger equation arising in the theory of water waves
• Resonant gravity-wave interactions in a shear flow

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