Envelope soliton solution for finite amplitude equatorial waves

Details Envelope soliton solution for finite amplitude equatorial waves Envelope soliton solution for finite amplitude equatorial waves

Nov 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ineps..90..305j&link_type=abstract

Proceedings of the Indian Academy of Sciences - Earth and Planetary Sciences, Volume 90, Issue 3, pp.305-326

Mathematics

Shallow Water Equations, Finite Amplitude Solutions, Multiple Time Scale Method, Envelope Solitons

Scientific paper

Using shallow water equations on an equatorial beta plane, the nonlinear dynamics of the equatorial waves is investigated. A general mathematical procedure to study the nonlinear dynamics of these waves is developed using the asymptotic method of multiple scales. On faster temporal and spatial scales the equations describe the equatorial waves viz, the Rossby waves, Rossby gravity waves, the inertia gravity waves and the Kelvin waves. Assuming that the amplitude of these waves are functions of slower time and space scales, it is shown that the evolution of the amplitude of these waves is governed by the nonlinear Schrodinger equation. It is then shown that for the dispersive waves like Rossby waves and Rossby-gravity waves, the envelope of the amplitude of the waves has a ‘soliton’ structure.

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