Abstract
| Language | English |
|---|---|
| Pages | 683-692 |
| Number of pages | 9 |
| Journal | Chaos, Solitons and Fractals |
| Volume | 17 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 2003 |
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Keywords
- Bäcklund transformation
- Vakhnenko equation
- solitons
- nonlinear equations
- inverse scattering
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A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. / Vakhnenko, V.O.; Parkes, E.J.; Morrison, A.J.
In: Chaos, Solitons and Fractals, Vol. 17, No. 4, 08.2003, p. 683-692.Research output: Contribution to journal › Article
TY - JOUR
T1 - A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
AU - Vakhnenko, V.O.
AU - Parkes, E.J.
AU - Morrison, A.J.
PY - 2003/8
Y1 - 2003/8
N2 - A Bäcklund transformation both in bilinear and in ordinary form for the transformed generalised Vakhnenko equation (GVE) is derived. It is shown that the equation has an infinite sequence of conservation laws. An inverse scattering problem is formulated; it has a third-order eigenvalue problem. A procedure for finding the exact N-soliton solution to the GVE via the inverse scattering method is described. The procedure is illustrated by considering the cases N=1 and 2.
AB - A Bäcklund transformation both in bilinear and in ordinary form for the transformed generalised Vakhnenko equation (GVE) is derived. It is shown that the equation has an infinite sequence of conservation laws. An inverse scattering problem is formulated; it has a third-order eigenvalue problem. A procedure for finding the exact N-soliton solution to the GVE via the inverse scattering method is described. The procedure is illustrated by considering the cases N=1 and 2.
KW - Bäcklund transformation
KW - Vakhnenko equation
KW - solitons
KW - nonlinear equations
KW - inverse scattering
UR - http://www.maths.strath.ac.uk/~caas35/vp&mCSF03.pdf
UR - http://dx.doi.org/10.1016/S0960-0779(02)00483-6
U2 - 10.1016/S0960-0779(02)00483-6
DO - 10.1016/S0960-0779(02)00483-6
M3 - Article
VL - 17
SP - 683
EP - 692
JO - Chaos, Solitons and Fractals
T2 - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
IS - 4
ER -