Abstract
Abstract In this article, the collective variable method to study two types of the Chen–Lee–Liu (CLL) equations, is employed. The CLL equation, which is also the second member of the derivative nonlinear Schrödinger equations, is known to have vast applications in optical fibers, in particular. More specifically, a consideration to the classical Chen–Lee–Liu (CCLL) and the perturbed Chen–Lee–Liu (PCLL) equations, is made. Certain graphical illustrations of the simulated numerical results that depict the pulse interactions in terms of the soliton parameters are provided. Also, the influential parameters in each model that characterize the evolution of pulse propagation in the media, are identified.
Highlights
Nonlinear Schrödinger equations are complex-valued timeevolving equations that are known to have a variety of applications in nonlinear sciences including biological models, optics, fluid dynamics, plasma physics, among other fields [1,2,3,4,5,6,7]
Different researchers have over a time employed the collective variable method to examine various evolution and Schrödinger equations. This method is relatively a new technique that splits the complex-valued wave function into two components and thereafter introduces new variables to characterize the dynamics of soliton propagation
(19) To determine the resulting dynamical equations of motions of the classical Chen–Lee–Liu (CCLL) equation given in equation (1), we first compute the entries of the matrix R with the help of Maple software as
Summary
Nonlinear Schrödinger equations are complex-valued timeevolving equations that are known to have a variety of applications in nonlinear sciences including biological models, optics, fluid dynamics, plasma physics, among other fields [1,2,3,4,5,6,7]. Different researchers have over a time employed the collective variable method to examine various evolution and Schrödinger equations. This method is relatively a new technique that splits the complex-valued wave function into two components and thereafter introduces new variables to characterize the dynamics of soliton propagation. The method gives the dynamics of each of the pulse parameter by utilizing the Gaussian ansatz to get hold of the resulting dynamical equations of motions for the subsequent examination. The subscripts in equations (1) and (2) are partial derivatives in the respective spatial and time variables
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