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Summary: This paper investigates a generalized Broer-Kaup-Kupershmidt system describing long waves in shallow water. By using symbolic computation, the authors establish a scaling transformation, a set of hetero-Backlund transformations, and two sets of similarity reductions from the generalized system to known linear and ordinary differential equations. The results depend on all the shallow-water coefficients.
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APPLIED MATHEMATICS LETTERS
(2022)
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APPLIED MATHEMATICS LETTERS
(2022)
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APPLIED MATHEMATICS LETTERS
(2022)
Review
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Mark J. Ablowitz et al.
Summary: In recent years, the study of wave propagation in nonlinear photonic lattices has attracted considerable interest. This review article focuses on the propagation of wave envelopes in periodic lattices associated with additional potential in the nonlinear Schrodinger equation. The tight-binding approximation is used to find the linear dispersion relation and the equations governing nonlinear discrete envelopes, and continuous envelope equations are derived from the discrete system in the limit of slowly varying envelopes. The article also explores the potential realization of topological insulator systems in an optical waveguide setting.
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PHYSICAL REVIEW LETTERS
(2021)
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