Optical solitons for Chen-Lee-Liu equation with two spectral collocation approaches. (English) Zbl 1478.78053

Summary: This paper revisits the study of optical solitons that is governed by one of the three forms of derivative nonlinear Schrödinger’s equation that is also known as Chen-Lee-Liu model. This model is investigated by the aid of fully shifted Jacobi’s collocation method with two independent approaches. The first is discretization of the spatial variable, while the other is discretization of the temporal variable. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.


78A60 Lasers, masers, optical bistability, nonlinear optics
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q41 Time-dependent Schrödinger equations and Dirac equations
35C08 Soliton solutions
78M22 Spectral, collocation and related methods applied to problems in optics and electromagnetic theory
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
Full Text: DOI


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