Fifth order evolution equation for long wave dissipative solitons |
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Authors: | M.C. Depassier J.A. Letelier |
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Affiliation: | Departamento de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile |
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Abstract: | Third and fifth order nonlinear wave equations which arise in the theory of water waves possess solitary and periodic traveling waves. Solitary waves also arise in systems with dissipation and instability where a balance between these effects allows the existence of dissipative solitons. Here we search for a model equation to describe long wave dissipative solitons including fifth order dispersion. The equation found includes quadratic and cubic nonlinearities. For periodic solutions in a small box we characterize the rate of growth, and show that they do not blow up in finite time. Analytic solutions are constructed for special parameter values. |
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Keywords: | Dissipative solitons Long wave instability Evolution equation |
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