The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1
- 7 August 1973
- journal article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 59 (4), 721-736
- https://doi.org/10.1017/s0022112073001813
Abstract
The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.This publication has 10 references indexed in Scilit:
- The Korteweg-de Vries equation and water waves. Part 2. Comparison with experimentsJournal of Fluid Mechanics, 1974
- An integral equation for unsteady surface waves and a comment on the Boussinesq equationJournal of Fluid Mechanics, 1971
- Integrals of nonlinear equations of evolution and solitary wavesCommunications on Pure and Applied Mathematics, 1968
- Solitons and Bound States of the Time-Independent Schrödinger EquationPhysical Review B, 1968
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967
- On the Interactions of Permanent Waves of Finite AmplitudeJournal of Mathematics and Physics, 1964
- Reflectionless Transmission through Dielectrics and Scattering PotentialsJournal of Applied Physics, 1956
- On the determination of a differential equation from its spectral functionAmerican Mathematical Society Translations: Series 2, 1955
- Quantum MechanicsAmerican Journal of Physics, 1949
- XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1895