A Numerical and Theoretical Study of Certain Nonlinear Wave Phenomena
Abstract
An efficient numerical method is developed for solving nonlinear wave equations typified by the Korteweg-de Vries equation and its generalizations. The method uses a pseudospectral (Fourier transform) treatment of the space dependence together with a leap-frog scheme in time. It is combined with theoretical discussions in the study of a variety of problems including solitary wave interactions, wave breaking, the resolution of initial steps and wells, and the development of nonlinear wavetrain instabilities.
- Publication:
-
Philosophical Transactions of the Royal Society of London Series A
- Pub Date:
- May 1978
- DOI:
- 10.1098/rsta.1978.0064
- Bibcode:
- 1978RSPTA.289..373F
- Keywords:
-
- Fourier Transformation;
- Nonlinear Equations;
- Numerical Analysis;
- Solitary Waves;
- Wave Equations;
- Wave Packets;
- Dynamic Stability;
- Error Analysis;
- Spatial Dependencies;
- Wave Interaction;
- Physics (General);
- WAVES;
- THEORY