Infinite generation of soliton-like solutions for complex nonlinear evolution differential equations via the NLSE-based constructive method

Dai, Chao-Qing; Wang, Yueyue

doi:10.1016/j.amc.2014.03.076

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…In recent decades, many direct methods have been proposed for obtaining exact solutions for non‐linear equations, such as tan( φ /2)‐expansion method, 8 the extended ( G ′ / G )‐expansion scheme, 9 the semi‐inverse variational principle, 10 Kudryashov method, 11 extended trial equation method, 12 elliptic function method, 13 the NLSE based constructive method, 14 first integral method, 15 simplest equation approach, 16 extended tanh function method, 17 extended F‐expansion method, 18 hyperbolic function method, 19 extended sinh‐Gordon equation method, 20 and many more 21‐28 . In this paper, the new EDAM 29‐32 and EHFM 33‐36 are used to retrieve the different types of solitons and some other solutions for 2D‐ CNLSE.…”

Section: Introductionmentioning

confidence: 99%

New soliton solutions of the 2D‐chiral nonlinear Schrodinger equation using two integration schemes

Rehman

Asjad

Bibi

et al. 2020

Math Methods in App Sciences

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In this paper, the new exact solutions for 2D‐chiral nonlinear Schrodinger equation (CNLSE) are acquired using two proficient integration tool, namely, the new extended direct algebraic method (EDAM) and extended hyperbolic function method (EHFM). We develop soliton and some other solutions by utilizing the particular values for the parameters involved in these methods. These methods are devoted to secure different kinds of new soliton solutions as well as trigonometric and hyperbolic function solutions. Furthermore, for the physical representation of the obtained solutions of the CNLSE, various 2D and 3D graphs are presented.

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Section: Introductionmentioning

confidence: 99%

New soliton solutions of the 2D‐chiral nonlinear Schrodinger equation using two integration schemes

Rehman

Asjad

Bibi

et al. 2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…In modern nonlinear sciences some of the most important models are the variable coefficient nonlinear Schrödinger-type ones. Applications include long distance optical communications, optical fibers and plasma physics, see [4], [5], [8], [12], [15], [23], [24], [25], [30], [41], [48], [49], [51], [52], [53], [61], [63], [65] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation

Escorcia

Suazo

2017

Applied Mathematics and Computation

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In this paper, by means of similarity transformations we study exact analytical solutions for a generalized nonlinear Schrödinger equation with variable coefficients. This equation appears in literature describing the evolution of coherent light in a nonlinear Kerr medium, Bose-Einstein condensates phenomena and high intensity pulse propagation in optical fibers. By restricting the coefficients to satisfy Ermakov-Riccati systems with multiparameter solutions, we present conditions for existence of explicit solutions with singularities and a family of oscillating periodic soliton-type solutions. Also, we show the existence of bright-, dark-and Peregrine-type soliton solutions, and by means of a computer algebra system we exemplify the nontrivial dynamics of the solitary wave center of these solutions produced by our multiparameter approach.

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Dark spatiotemporal optical solitary waves in self-defocusing nonlinear media

2016

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Infinite generation of soliton-like solutions for complex nonlinear evolution differential equations via the NLSE-based constructive method

Cited by 6 publications

References 23 publications

New soliton solutions of the 2D‐chiral nonlinear Schrodinger equation using two integration schemes

New soliton solutions of the 2D‐chiral nonlinear Schrodinger equation using two integration schemes

Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation

Dark spatiotemporal optical solitary waves in self-defocusing nonlinear media

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