Soliton production and solutions to perturbed Korteweg-deVries equations
- 1 January 1980
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 21 (1) , 335-339
- https://doi.org/10.1103/physreva.21.335
Abstract
The author discusses the production of a secondary soliton when the wave equation describing the soliton undergoes a small perturbation. Discussion is limited to the Korteweg-deVries equation, where it is found that, for an appropriate sign of the perturbation, soliton production always occurs. The methods of inverse scattering are used where this production can be clearly demonstrated. Previous authors have ignored the production of secondary solitons and consequently have arrived at erroneous conclusions regarding the conservation laws. Two examples of perturbations are discussed in some detail.Keywords
This publication has 11 references indexed in Scilit:
- Interaction of perturbed solitons and the structure of oscillatory shocksPhysics Letters A, 1979
- Higher Order Approximation in the Reductive Perturbation Method. I. The Weakly Dispersive SystemJournal of the Physics Society Japan, 1978
- Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theoryProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Collapse of a Korteweg de Vries soliton into a weak noise shelfPhysics Letters A, 1978
- Korteweg-de Vries Soliton in a Slowly Varying MediumPhysical Review Letters, 1978
- Solitons under perturbationsPhysical Review A, 1977
- A perturbation theory for the Korteweg-De Vries equationPhysics Letters A, 1977
- Inverse Problems in Quantum Scattering TheoryPublished by Springer Nature ,1977
- Korteweg-de Vries equation: A completely integrable Hamiltonian systemFunctional Analysis and Its Applications, 1972
- XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesJournal of Computers in Education, 1895