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Soliton dynamics of a discrete integrable Ablowitz-Ladik equation for some electrical and optical systems. (English) Zbl 1325.39006
Summary: Under investigation in this paper is a discrete integrable Ablowitz-Ladik equation, which has certain applications in the electrical and optical systems. Via the Hirota method and symbolic computation, the bilinear forms and \(N\)-bright soliton solutions are obtained. Propagation and interaction behaviors of the discrete solitons are analyzed through the one- and two-soliton solutions. The discreteness effects on soliton and soliton interaction are discussed. Asymptotic analysis shows that the interactions between two solitons are elastic. Head-on and overtaking interactions can be obtained with the choices of the directions of the velocities. Two kinds of overtaking interactions are investigated analytically and graphically, respectively.

39A12 Discrete version of topics in analysis
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35C08 Soliton solutions
35Q55 NLS equations (nonlinear Schrödinger equations)
Full Text: DOI
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