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Darboux transformation and soliton solutions for the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics. (English) Zbl 1335.35239

Summary: In this paper, by virtue of the Darboux transformation (DT) and symbolic computation, the quintic generalization of the coupled cubic nonlinear Schrödinger equations from twin-core nonlinear optical fibers and waveguides are studied, which describe the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media. Lax pair of the equations is obtained and the corresponding DT is constructed. Moreover, one-, two- and three-soliton solutions are presented in the forms of modulus. Features of solitons are graphically discussed: (1) head-on and overtaking elastic collisions of the two solitons; (2) periodic attraction and repulsion of the bounded states of two solitons; (3) energy-exchanging collisions of the three solitons.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C08 Soliton solutions
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