Generalized Solutions to the Korteweg–de Vries and the Regularized Long-Wave Equations
- 1 July 1992
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 23 (4) , 923-940
- https://doi.org/10.1137/0523049
Abstract
In this article generalized solutions to two model equations describing nonlinear dispersive waves are studied. The solutions are found in certain algebras of new generalized functions containing spaces of distributions. On the one hand, this allows the handling of initial data with strong singularities. On the other hand, suitable scaling allows one to introduce an infinitesimally small coefficient; thereby the authors produce generalized solutions in the sense of Colombeau to the inviscid Burgers equation.Keywords
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