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Darboux transformation and soliton solutions for inhomogeneous coupled nonlinear Schrödinger equations with symbolic computation. (English) Zbl 1186.35213

Summary: With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrödinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e., Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
35C08 Soliton solutions
35A30 Geometric theory, characteristics, transformations in context of PDEs
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
78A10 Physical optics
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