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Integrable semi-discretization of a multi-component short pulse equation. (English) Zbl 1315.35201

Summary: In the present paper, we mainly study the integrable semi-discretization of a multi-component short pulse equation. First, we briefly review the bilinear equations for a multi-component short pulse equation proposed by Y. Matsuno [ibid. 52, No. 12, 123702, 22 p. (2011; Zbl 1273.78014)] and reaffirm its \(N\)-soliton solution in terms of pfaffians. Then by using a Bäcklund transformation of the bilinear equations and defining a discrete hodograph (reciprocal) transformation, an integrable semi-discrete multi-component short pulse equation is constructed. Meanwhile, its \(N\)-soliton solution in terms of pfaffians is also proved.{
©2015 American Institute of Physics}

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
78A60 Lasers, masers, optical bistability, nonlinear optics
81V80 Quantum optics
35Q60 PDEs in connection with optics and electromagnetic theory
35C08 Soliton solutions
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
39A12 Discrete version of topics in analysis

Citations:

Zbl 1273.78014
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References:

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