## 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
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### References:

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