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A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and Darboux transformation. (English) Zbl 1328.37054

Summary: A deformed reduced semi-discrete Kaup-Newell equation and its related integrable family are derived from discrete zero curvature equation. A Darboux transformation of Lax pair of this equation is established with the help of gauge transformation. By means of the resulting Darboux transformation, three exact solutions are given.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35Q53 KdV equations (Korteweg-de Vries equations)
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