Existence of solutions for a class of edge wave equations

DOI10.3934/DCDSB.2006.6.1113zbMath1115.76015OpenAlexW2319641420MaRDI QIDQ862126

Octavian G. Mustafa, David Henry

Publication date: 5 February 2007

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2006.6.1113

zbMATH Keywords

Banach contraction principleKrasnoselskii fixed point theorem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

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Instability of equatorial edge waves in the background flow ⋮ Exact solution and instability for geophysical edge waves ⋮ Edge waves with longshore currents ⋮ An exact solution for geophysical edge waves in the \(f\)-plane approximation ⋮ Instability of edge waves along a sloping beach ⋮ Two-dimensional steady edge waves. I: Periodic waves ⋮ Two-dimensional steady edge waves. II: Solitary waves ⋮ Short-wavelength instabilities of edge waves in stratified water ⋮ An exact solution for nonlinear internal equatorial waves in the \(f\)-plane approximation ⋮ An exact solution for geophysical internal waves with underlying current in modified equatorial β-plane approximation* ⋮ Exact solution and instability for geophysical waves in modified equatorial \(\beta\)-plane approximation with and without centripetal forces ⋮ Exact azimuthal equatorially trapped waves with centripetal force in modified equatorial \(\beta\)-plane approximation and at arbitrary latitude

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