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Three-dimensional nonlinear Schrödinger equation for finite-amplitude gravity waves in a fluid

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Il Nuovo Cimento B (1971-1996)

Summary

The averaged Lagrangian method is used to derive a new nonlinear Schrödinger equation in order to describe the evolution of three-dimensional modulations superposed on finite-amplitude gravity waves in a fluid. An interesting feature of this equation is that the wave energy initially confined to a narrow band of wave numbers continues to be confined to a limited region in the wave number space. Unlike the three-dimensional nonlinear evolution equation available in the literature, the equation obtained in this paper may, therefore, be adequate for the description of the evolution of the three-dimensional modulations.

Riassunto

II metodo lagrangiano mediato è usato per derivare una nuova equazione nonlineare di Schrödinger per descrivere l'evoluzione delle modulazioni tridimensionali sovrapposte ad onde gravitazionali di ampiezza finita in un fluido. Una caratteristica interessante di questa equazione è che l'energia d'onda inizialmente confinata in una stretta banda di numeri d'onda continua ad essere confinata in una regione limitata nello spazio del numero d'onda. Diversamente dall'equazione di evoluzione nonlineare tridimensionale disponibile nella letteratura, l'equazione ottenuta in questo lavoro può, perciò, essere adeguata alla descrizione dell'evoluzione delle modulazioni tridimensionali.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, 32816, Orlando, FL

    B. K. Shivamoggi & L. Debnath

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  1. B. K. Shivamoggi
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  2. L. Debnath
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Shivamoggi, B.K., Debnath, L. Three-dimensional nonlinear Schrödinger equation for finite-amplitude gravity waves in a fluid. Nuov Cim B 94, 140–148 (1986). https://doi.org/10.1007/BF02759753

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