Analytical insights into a generalized semidiscrete system with time-varying coefficients: derivation, exact solutions, and nonlinear soliton dynamics. (English) Zbl 1506.37093
Summary: In this paper, a new generalized semidiscrete integrable system with time-varying coefficients is analytically studied. Firstly, the generalized semidiscrete system is derived from a semidiscrete matrix spectral problem by embedding finite time-varying coefficient functions. Secondly, exact and explicit \(N\)-soliton solutions of the semidiscrete system are obtained by using the inverse scattering analysis. Finally, three special cases when \(N=1,2,3\) of the obtained \(N\)-soliton solutions are simulated by selecting some appropriate coefficient functions. It is shown that the time-varying coefficient functions affect the spatiotemporal structures and the propagation velocities of the obtained semidiscrete one-soliton solutions, two-soliton solutions, and three-soliton solutions.
MSC:
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 35Q51 | Soliton equations |
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