dorsal/arxiv
View SchemaAsymptotic dynamics of short-waves in nonlinear dispersive models
| Authors | M. A. Manna, V. Merle |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9710013 |
| URL | https://arxiv.org/abs/solv-int/9710013 |
| DOI | 10.1103/PhysRevE.57.6206 |
Abstract
The multiple-scale perturbation theory, well known for long-waves, is extended to the study of the far-field behaviour of short-waves, commonly called ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation can propagates short-waves. This result contradict the Benjamin hypothesis that short-waves tends not to propagate in this model and close a part of the old controversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine equations. We shown that a nonlinear (quadratic) Klein-Gordon type equation substitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation of long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon equations are understood as an all orders asymptotic behaviour of short-waves. It is proved that the antikink solution of phi-4 model which was never obtained perturbatively can be obtained by perturbation expansion in the wave-number k in the short-wave limit.
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"abstract": "The multiple-scale perturbation theory, well known for long-waves, is\nextended to the study of the far-field behaviour of short-waves, commonly\ncalled ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation\ncan propagates short-waves. This result contradict the Benjamin hypothesis that\nshort-waves tends not to propagate in this model and close a part of the old\ncontroversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine\nequations. We shown that a nonlinear (quadratic) Klein-Gordon type equation\nsubstitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation\nof long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon\nequations are understood as an all orders asymptotic behaviour of short-waves.\nIt is proved that the antikink solution of phi-4 model which was never obtained\nperturbatively can be obtained by perturbation expansion in the wave-number k\nin the short-wave limit.",
"arxiv_id": "solv-int/9710013",
"authors": [
"M. A. Manna",
"V. Merle"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1103/PhysRevE.57.6206",
"title": "Asymptotic dynamics of short-waves in nonlinear dispersive models",
"url": "https://arxiv.org/abs/solv-int/9710013"
},
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