Classical Boussinesq Equation is a Reduction of the Modified KP Equation
Abstract
The classical Boussinesq equation ut{=}[(1+u)v+vxx]x, vt{=}(u+v2/2)x describing shallow water waves, is transformed into the bilinear form and is shown to be a “pq{=}const” reduction of the modified KP equation. It is also shown that the bilinear form of the classical Boussinesq equation is transformed into the non-linear Schrödinger equation exhibiting dark-soliton solution.
- Publication:
-
Journal of the Physical Society of Japan
- Pub Date:
- July 1985
- DOI:
- 10.1143/JPSJ.54.2409
- Bibcode:
- 1985JPSJ...54.2409H
- Keywords:
-
- Boussinesq Approximation;
- Water Waves;
- Wave Equations;
- Schroedinger Equation;
- Shallow Water;
- Solitary Waves;
- Transformations (Mathematics);
- Physics (General)