Asymptotic Solutions of the Korteweg‐deVries Equation
- 1 July 1977
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 57 (1) , 13-44
- https://doi.org/10.1002/sapm197757113
Abstract
The long‐time asymptotic solution of the Korteweg‐deVries equation, corresponding to initial data which decay rapidly as |x|→∞ and produce no solitons, is found to be considerably more complicated than previously reported. In general, the asymptotic solution consists of exponential decay, similarity, rapid oscillations and a “collisionless shock” layer. The wave amplitude in this layer decays as [(lnt)/t]2/3. Only for very special initial conditions is the shock layer absent from the solution.Keywords
This publication has 12 references indexed in Scilit:
- Asymptotic solutions and conservation laws for the nonlinear Schrödinger equation. IIJournal of Mathematical Physics, 1976
- Asymptotic solutions and conservation laws for the nonlinear Schrödinger equation. IJournal of Mathematical Physics, 1976
- Korteweg-de Vries Equation; Asymptotic Behavior of SolutionsPublications of the Research Institute for Mathematical Sciences, 1974
- Korteweg‐devries equation and generalizations. VI. methods for exact solutionCommunications on Pure and Applied Mathematics, 1974
- The decay of the continuous spectrum for solutions of the Korteweg-deVries equationJournal of Mathematical Physics, 1973
- The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1Journal of Fluid Mechanics, 1973
- Korteweg-de Vries equation: A completely integrable Hamiltonian systemFunctional Analysis and Its Applications, 1972
- A non-linear equation incorporating damping and dispersionJournal of Fluid Mechanics, 1970
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial StatesPhysical Review Letters, 1965