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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.

MSC:
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)
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