A modified regularized long-wave equation with an exact two-soliton solution
- 1 October 1976
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 9 (10) , L127-L130
- https://doi.org/10.1088/0305-4470/9/10/002
Abstract
Numerical studies of the regularized long-wave (RLW) equation ut+ux+(6u2-uxt)x=0 suggests it has a two-soliton solution although an analytic form for this has not yet been found. The authors show that a modified form of the RLW equation ut+ux+(4u2+2wxvt-uxt)x=0, with u=wt=vx, has an exact two-soliton solution. The modified equation has the same solitary-wave solution as the original equation and its analytic two-soliton solution agrees closely with the numerical solution of the RLW equation.Keywords
This publication has 7 references indexed in Scilit:
- N-Soliton Solutions of Nonlinear Network Equations Describing a Volterra SystemJournal of the Physics Society Japan, 1976
- N-Soliton Solutions of Model Equations for Shallow Water WavesJournal of the Physics Society Japan, 1976
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear ProblemsStudies in Applied Mathematics, 1974
- The soliton: A new concept in applied scienceProceedings of the IEEE, 1973
- Model equations for long waves in nonlinear dispersive systemsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1972
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of SolitonsPhysical Review Letters, 1971
- Calculations of the development of an undular boreJournal of Fluid Mechanics, 1966