×

Soliton solutions and Bäcklund transformation for the Kupershmidt five-field lattice: A bilinear approach. (English) Zbl 1009.37047

Summary: The Kupershmidt five-field lattice is considered. By a dependent variable transformation, the Kupershmidt lattice is transformed into a bilinear form by the introduction of three auxiliary variables. We present a Bäcklund transformation and a nonlinear superposition formula for the Kupershmidt lattice. As an application of the results, soliton solutions are derived.

MSC:

37K60 Lattice dynamics; integrable lattice equations
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q51 Soliton equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Kupershmidt, B.A., Discrete Lax equations and differential-difference calculus, Astérisque, 123, 212, (1985) · Zbl 0565.58024
[2] Blaszak, M.; Marciniak, K., r-matrix approach to lattice integrable systems, J. math. phys., 35, 4661-4682, (1994) · Zbl 0823.58013
[3] Hu, X.B.; Zhu, Z.N., Some new results on the blaszak-marciniak lattice: Bäcklund transformation and nonlinear superposition formula, J. math. phys., 39, 4766-4772, (1998) · Zbl 0927.37050
[4] Ma, W.X.; Hu, X.B.; Zhu, S.M.; Wu, Y.T., Bäcklund transformation and its superposition principle of a blaszak-marciniak four-field lattice, J. math. phys., 40, 6071-6086, (1999) · Zbl 1063.37564
[5] Hirota, R., Direct methods in soliton theory, () · Zbl 0124.21603
[6] Hirota, R.; Satsuma, J., A variety of nonlinear network equations generated from the Bäcklund transformation for the Toda lattice, Prog. theor. phys. suppl., 59, 64-100, (1976)
[7] Matsuno, Y., ()
[8] Nimmo, J.J.C., Hirota’s method, () · Zbl 0743.35074
[9] Hietarinta, J., A search for bilinear equations passing Hirota’s three-soliton condition, J. math. phys., 28, 1732-1742, (1987) · Zbl 0641.35073
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.