×

Darboux transformation and soliton solutions for generalized WKI equations. (English) Zbl 1141.35456

Summary: A systematic method is presented to construct the Darboux transformation for generalized WKI equations. With the aid of symbolic computation, new soliton-like solutions for the GWKI equations are obtained by using its Darboux transformation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
Full Text: DOI

References:

[1] DOI: 10.1137/1.9781611970883 · doi:10.1137/1.9781611970883
[2] Novikov S. P., Theory of Solitons, the Inverse Scattering Methods (1984)
[3] DOI: 10.1143/JPSJ.46.1965 · Zbl 1334.81106 · doi:10.1143/JPSJ.46.1965
[4] Gu C. H., Darboux Transformation in Soliton Theory and Its Geometric Applications (1999)
[5] DOI: 10.1007/978-3-662-00922-2 · doi:10.1007/978-3-662-00922-2
[6] DOI: 10.1088/0305-4470/16/9/017 · doi:10.1088/0305-4470/16/9/017
[7] DOI: 10.1016/0375-9601(84)90827-2 · doi:10.1016/0375-9601(84)90827-2
[8] DOI: 10.1088/0266-5611/4/1/014 · Zbl 0701.34036 · doi:10.1088/0266-5611/4/1/014
[9] Zhou Z. X., Lett. Math. Phys. 16 pp 9–
[10] Gu C. H., Lett. Math. Phys. 35 pp 61–
[11] Cieslinski J., J. Math. Phys. 36 pp 1567–
[12] DOI: 10.1063/1.532811 · Zbl 0943.35078 · doi:10.1063/1.532811
[13] DOI: 10.1016/S0960-0779(03)00385-0 · Zbl 1045.37038 · doi:10.1016/S0960-0779(03)00385-0
[14] DOI: 10.1063/1.1314895 · Zbl 0986.37059 · doi:10.1063/1.1314895
[15] DOI: 10.1016/j.chaos.2005.01.030 · Zbl 1078.35118 · doi:10.1016/j.chaos.2005.01.030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.