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Article Dans Une Revue Physics of Fluids Année : 1995

Two-level solitary waves as generalized solutions of the KdV equation

Résumé

An analyticai class of standing wave solutions to the Korteweg-de Vries (KdV) equation is obtained in the framework of continuous finite generalized functions. This paper shows how this class can be used to describe a great variety of wave shapes, especially bores and jumps. These new solutions are built by appropriately combining parts of two ordinary KdV waves. These represent a system with a steep transition between different energy levels of two potential wells. A number of specifie cases of the generalized solutions are identical to those obtained recently within the theory of the KdV equation forced by a Dirac delta function. Numerical simulations of both stationary and transient KdV equations are carried out in a few cases. The weak formulation used in the numerical scheme is equivalent to the analytical generalized functions approach. Simulations of initially perturbed wave fronts prove the high degree of stability of many of these solutions.
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Dates et versions

hal-01643980 , version 1 (21-11-2017)

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B Izrar, F. Lusseyran, V Miroshnikov. Two-level solitary waves as generalized solutions of the KdV equation. Physics of Fluids, 1995, 7 (5), pp.1056-1062. ⟨10.1063/1.868548⟩. ⟨hal-01643980⟩
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