The exact solutions and the relevant constraint conditions for two nonlinear Schrödinger equations with variable coefficients

Zhang, Jinliang; Li, Baoan; Wang, Mingliang

doi:10.1016/j.chaos.2007.01.116

Cited by 24 publications

(5 citation statements)

References 34 publications

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“…An equation with an additional quintic nonlinearity when the coefficient functions mostly depend on time models the propagation of pulses in optic fibers and was studied in [3], where trigonometric type solutions were obtained through some transformations. [4] studies the equation with space and time coordinates switched, modeling propagation of pulses in optical fibers with distributed dispersion and nonlinearity and finds soliton-type solutions with a Darboux transformation, whereas elliptic-type solutions through various transformations [5], soliton-type solutions via Hirota method [6] and in terms of a double-Wronskian determinant [7], and self-similar solutions also exist in the literature [8]. In these works, the coefficients are considered as functions of a single variable.…”

Section: Introductionmentioning

confidence: 99%

On Integrability of Variable Coefficient Nonlinear Schrödinger Equations

Özemir

Güngör

2012

Rev. Math. Phys.

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We apply Painlevé test to the most general variable coefficient nonlinear Schrödinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by the use of other tools like group-theoretical approach and the Lax pairs technique of the soliton theory. We present explicit transformation formulae that can be used to generate new analytic solutions of VCNLS equations from those of the integrable NLS equation.

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Section: Introductionmentioning

confidence: 99%

On Integrability of Variable Coefficient Nonlinear Schrödinger Equations

Özemir

Güngör

2012

Rev. Math. Phys.

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“…This paper demonstrates new types of wave solutions for the generalized derivative NLSE with varying coefficients (Vc-GDNLSE) [28] via an efficient technique, namely the unified method [29,30]. In this case, when the nonlinearity parameter and dispersion coefficient are treated as variable functions in optical communication, the NLSE model with variable coefficients simulates significant phenomena [31]. The Vc-GDNLSE has the following structure [28].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Properties of Non-Autonomous Femtosecond Waves Modeled by the Generalized Derivative NLSE with Variable Coefficients

et al. 2022

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The primary purpose of this study is to analyze non-autonomous femtosecond waves with various geometrical configurations correlated to the generalized derivative nonlinear Shrödinger equation (NLSE) with variable coefficients. Numerous academic publications, especially in nonlinear optics, material science, semiconductor, chemical engineering, and many other fields, have looked into this model since it is closer to real-world situations and has more complex wave structures than models with constant coefficients. It can serve as a reflection for the slowly altering inhomogeneities, non-uniformities, and forces acting on boundaries. New complex wave solutions in two different categories are proposed: implicit and elliptic (or periodic or hyperbolic) forms are obtained for this model via the unified method. Indeed, the innovative wave solutions that were achieved and reported here are helpful for investigating optical communication applications as well as the transmission characteristics of light pulses.

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“…Solving variable coefficient NLEEs is much more difficult than their constant coefficient counterparts because of the existence of their coefficient function. Recently, much attention has been paid to variable coefficient NLS equations, [27][28][29][30][31][32] and many techniques and approaches have been extended to solve these physical models.…”

Section: Introductionmentioning

confidence: 99%