Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity

Srivástava, H. M.; Günerhan, Hatıra; Ghanbari, Behzad

doi:10.1002/mma.5827

Cited by 114 publications

(33 citation statements)

References 14 publications

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“…Finding the value of k and then inserting Equations (10) and (12) into Equation (9), we get a system of terms of:…”

Section: The Extended Shgemmentioning

confidence: 99%

“…respectively. Inserting Equation (22) along with Equation (12) into Equation (21), and using constraint conditions provides a non-linear algebraic system. Equaling each coefficient of sinh i (θ ) cosh j ( θ ) with the same power to zero, and finding the obtained system of algebraic equations, we gain the values of the parameters.…”

Section: Implement Of the Extended Shgemmentioning

confidence: 99%

“…The non-linear Schrödinger equation is a generalized (1+1)-dimensional version of the Ginzburg-Landau equation presented in 1950 in their study on supraconductivity and has been specifically reported by Chiao et al [1] in their research of optical beams. In the past several years, various methods have been proposed to obtain the exact optical soliton solutions of the non-linear Schrödinger equation [2][3][4][5][6][7][8][9][10][11][12]. Dispersion and non-linearity are two of the essential components for the distribution of solitons across inter-continental regions.…”

Section: Introductionmentioning

confidence: 99%

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Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

et al. 2020

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The research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon expansion method. This method is one of the strongest methods to find the exact solutions to the non-linear partial differential equations. In order to confirm the existing solutions, the constraint conditions are used. We successfully construct various exact solitary wave solutions to the governing equation, for example, singular, and dark-bright solutions. Moreover, the 2D, 3D, and contour surfaces of all obtained solutions are also plotted. The finding solutions have justified the efficiency of the proposed method.

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“…Finding the value of k and then inserting Equations (10) and (12) into Equation (9), we get a system of terms of:…”

Section: The Extended Shgemmentioning

confidence: 99%

Section: Implement Of the Extended Shgemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

et al. 2020

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“…To continue our investigation, we distinguish two cases: a < 0 or a > 0. Firstly, we assume that a < 0 (a = −a 0 , a 0 > 0) and in (27) and that α + a 0 > 0. If α + a 0 < 0 or α < −a 0 , then the solution is stable.…”

Section: Stability Of Stationary Traveling Waves (Pulses)mentioning

confidence: 99%

“…One can construct solutions u(α, x) of the Equations (27) and (30), which satisfy the following limit relationship: lim…”

Section: A Set Of Examplesmentioning

confidence: 99%

Stability of Traveling Waves Based upon the Evans Function and Legendre Polynomials

2020

Self Cite

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One of the tools and techniques concerned with the stability of nonlinear waves is the Evans function which is an analytic function whose zeros give the eigenvalues of the linearized operator. Here, in this paper, we propose a direct approach, which is based essentially upon constructing the eigenfunction solution of the perturbed equation based upon the topological invariance in conjunction with usage of the Legendre polynomials, which have presumably not considered in the literature thus far. The associated Legendre eigenvalue problem arising from the stability analysis of traveling waves solutions is systematically studied here. The present work is of considerable interest in the engineering sciences as well as the mathematical and physical sciences. For example, in chemical industry, the objective is to achieve a great yield of a given product. This can be controlled by depicting the initial concentration of the reactant, which is determined by its value at the bifurcation point. This analysis leads to the point separating stable and unstable solutions. As far as chemical reactions are described by reaction-diffusion equations, this specific concentration can be found mathematically. On the other hand, the study of stability analysis of solutions may depict whether or not a soliton pulse is well-propagated in fiber optics. This can, and should, be carried out by finding the solutions of the coupled nonlinear Schrödinger equations and by analyzing the stability of these solutions.

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New mathematical approaches to nonlinear coupled Davey–Stewartson Fokas system arising in optical fibers

Wang

2024

Math Methods in App Sciences

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This research focuses on the nonlinear coupled Davey–Stewartson Fokas system, which models pulse propagation in monomode optical fibers. In order to find the novel periodic and solitary wave solutions of the nonlinear coupled Davey–Stewartson Fokas system, we have employed two effective mathematical techniques named as the Sine‐Gordon expansion method and the simple equation method. We found after researching into previous literature that these novel solutions are unique and have never been reported. Some 3D and 2D graphs are also used to discuss the dynamical behavior of these new solutions.

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Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity

Cited by 114 publications

References 14 publications

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

Stability of Traveling Waves Based upon the Evans Function and Legendre Polynomials

New mathematical approaches to nonlinear coupled Davey–Stewartson Fokas system arising in optical fibers

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