Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis
TL;DR: In this paper, a modified simple equation method is employed to the nonlinear higher order Schrodinger equations for soliton solutions, which is applicable to solve different kind of problems in mathematics and physics.
About: This article is published in Optik.The article was published on 2017-09-01. It has received 137 citations till now. The article focuses on the topics: Nonlinear Schrödinger equation & Soliton.
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TL;DR: In this paper, the authors reveal the dark, bright, mixed dark-bright, singular and mixed singular optical solitons to the space-time fractional (1+1)-dimensional coupled nonlinear Schrodinger equation by using the extended sinh-Gordon equation expansion method.
139 citations
TL;DR: In this article, the exact travelling wave solutions of the system of equations for the ion sound and Langmuir waves (SEISLWs) were derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of SEISLW.
Abstract: We investigated the new exact travelling wave solutions of the system of equations for the ion sound and Langmuir waves (SEISLWs). In this work, we use the extended form of two methods, auxiliary equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs. These new exact travelling solutions are derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of the SEISLWs. We used the Mathematica program to show these solutions in two and three dimensions graphically.
138 citations
116 citations
TL;DR: In this article, the higher order non-linear Schrodinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses in optical fibers and the obtained solutions have key applications in physics and mathematics.
100 citations
TL;DR: In this paper, the authors discussed analytically higher order dispersive extended nonlinear Schrodinger equation with the aid of newly developed technique named as extended modified auxiliary equation mapp...
Abstract: In this paper, we discussed analytically higher order dispersive extended nonlinear Schrodinger equation with the aid of newly developed technique named as extended modified auxiliary equation mapp...
99 citations
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Book•
01 Jan 1989TL;DR: The field of nonlinear fiber optics has advanced enough that a whole book was devoted to it as discussed by the authors, which has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field.
Abstract: Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers. Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first used to generate the second-harmonic radiation inside a crystal [1], the use ofoptical fibers as a nonlinear medium became feasible only after 1970 when fiber losses were reduced to below 20 dB/km [2]. Stimulated Raman and Brillouin scatterings in single-mode fibers were studied as early as 1972 [3] and were soon followed by the study of other nonlinear effects such as self- and crossphase modulation and four-wave mixing [4]. By 1989, the field ofnonlinear fiber optics has advanced enough that a whole book was devoted to it [5]. This book or its second edition has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field of nonlinear fiber optics.
15,770 citations
Book•
01 Dec 1981
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
Abstract: : Under appropriate conditions, ocean waves may be modeled by certain nonlinear evolution equations that admit soliton solutions and can be solved exactly by the inverse scattering transform (IST). The theory of these special equations is developed in five lectures. As physical models, these equations typically govern the evolution of narrow-band packets of small amplitude waves on a long (post-linear) time scale. This is demonstrated in Lecture I, using the Korteweg-deVries equation as an example. Lectures II and III develop the theory of IST on the infinite interval. The close connection of aspects of this theory to Fourier analysis, to canonical transformations of Hamiltonian systems, and to the theory of analytic functions is established. Typical solutions, including solitons and radiation, are discussed as well. With periodic boundary conditions, the Korteweg-deVries equation exhibits recurrence, as discussed in Lecture IV. The fifth lecture emphasizes the deep connection between evolution equations solvable by IST and Painleve transcendents, with an application to the Lorenz model.
3,415 citations
TL;DR: Based on the homogeneous balance method, a simple and efficient method for obtaining exact solutions of nonlinear partial differential equations is proposed in this paper, where some equations are investigated by this means and new solitary wave solutions or singular traveling wave solutions are found.
543 citations
TL;DR: The proposed algorithm has been successfully tested on two very important evolution equations namely Fitzhugh–Nagumo equation and Sharma–Tasso–Olver equation and results are very encouraging.
398 citations
TL;DR: In this article, the tan-h method is applied to the Dodd-Bullough-Mikhailov and Tzitzeica-Dodd-bullough equations and periodic solutions for these equations are formally derived.
Abstract: The tan h method is applied to the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Solitons and periodic solutions for these equations are formally derived. The Painleve property v = e ± u will be employed to back up our analysis and to emphasize the effectiveness of the presented method.
290 citations