A Bäcklund transformation and nonlinear superposition formula of a modified Korteweg–de Vries-type bilinear equation
Author:
- 1 September 1994
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 35 (9) , 4739-4745
Abstract
A modified Korteweg–de Vries (mKdV)-type bilinear equation that has been shown to pass the three-soliton solution and the Painlevé tests [see, J. Math. Phys. 2094, 28 (1987); 2572, 31 (1990)] is considered herein. In this article, a Bäcklund transformation and a nonlinear superposition formula are proven rigorously. As an application of the obtained results, N-soliton solutions are obtained. Therefore, the integrability of this mKdV-type bilinear equation is confirmed.Keywords
This publication has 10 references indexed in Scilit:
- A search for bilinear equations passing Hirota’s three-soliton condition. IV. Complex bilinear equationsJournal of Mathematical Physics, 1988
- Superposition formulae of a fifth order KdV equation and its modified equationActa Mathematicae Applicatae Sinica, English Series, 1988
- A search for bilinear equations passing Hirota’s three-soliton condition. III. Sine–Gordon-type bilinear equationsJournal of Mathematical Physics, 1987
- A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equationsJournal of Mathematical Physics, 1987
- A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equationsJournal of Mathematical Physics, 1987
- Decay mode solution of the two-dimensional KdV equation and the generalized Bäcklund transformationJournal of Mathematical Physics, 1981
- Bäcklund Transformation of the Cylindrical KdV EquationJournal of the Physical Society of Japan, 1980
- Bäcklund Transform and Conservation Laws of the Benjamin-Ono EquationJournal of the Physical Society of Japan, 1979
- A Simple Structure of Superposition Formula of the Bäcklund TransformationJournal of the Physical Society of Japan, 1978
- A New Form of Backlund Transformations and Its Relation to the Inverse Scattering ProblemProgress of Theoretical Physics, 1974