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High-order evolution equation for nonlinear wave-packet propagation with surface tension accountingÉquation d'évolution d'ordre élevé de groupes d'ondes non linéaires en présence de tension superficielle |
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| Authors: | Igor Selezov Olga Avramenko Christian Kharif Karsten Trulsen |
| Affiliation: | 1. Department of Wave Processes, Institute of Hydromechanics, NAS of Ukraine, Kiev, Ukraine;2. Mathematical Department, Kirovograd State Pedagogical University, Kirovograd, Ukraine;3. Institut de recherche sur les phénomènes hors équilibre, 49, rue F. Joliot-Curie, BP 146, 13384 Marseille cedex 13, France;4. University of Oslo, Department Mathematics, Oslo, Norway |
| Abstract: | The nonlinear problem for propagation of wave-packets along the interface of two semi-infinite fluids is solved on the basis of multiple scale asymptotic expansions. Unlike all previous investigations dealing only with third-order approximations, here fourth-order approximation is developed. The corresponding solvability condition is obtained and the evolution equation in the case away from the cut-off wave number is derived. As a result, the nonlinear higher-order Schrödinger equation is obtained which contains the nonlinear part in a compact form. This equation is valid for a wide range of wave numbers. The stability diagram shows regions of stability and instability of capillary-gravity wave-packets. To cite this article: I. Selezov et al., C. R. Mecanique 331 (2003). |
| Keywords: | Waves Wave-packets Multiple scales Fourth-order problem Evolution equation Ondes Groupe d'ondes Échelles multiples Problème au quatrième ordre Équation d'évolution |
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