Bifurcation and new exact traveling wave solutions to time-space coupled fractional nonlinear Schrödinger equation

Han, Tianyong; Li, Zhao; Zhang, Xue

doi:10.1016/j.physleta.2021.127217

Cited by 55 publications

(18 citation statements)

References 30 publications

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“…Remark 2. Obviously (see [16][17][18][19][20]), all traveling wave solutions of ( 1) can be obtained from the phase orbits of the Hamiltonian system (9) according to Lemma 1.…”

Section: Bifurcations Of Phase Portraits Of System (9)mentioning

confidence: 99%

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Zhao

Han

2021

Advances in Mathematical Physics

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In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.

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“…Remark 2. Obviously (see [16][17][18][19][20]), all traveling wave solutions of ( 1) can be obtained from the phase orbits of the Hamiltonian system (9) according to Lemma 1.…”

Section: Bifurcations Of Phase Portraits Of System (9)mentioning

confidence: 99%

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Zhao

Han

2021

Advances in Mathematical Physics

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“…e exact traveling wave solutions of fractional partial differential equations have attracted much attention from mathematicians and engineering experts [1][2][3][4][5][6][7][8][9][10]. In recent years, some methods for constructing fractional partial differential equations have been proposed, such as the fractional double function method [11], improved fractional subequation method [12], (G ′ /G1/G)-expansion method [13], plane dynamic system analysis method [14], and complete discrimination method of polynomial [15].…”

Section: Introductionmentioning

confidence: 99%

New Classifications of All Single Traveling Wave Solutions of the Fractional Approximate Long Water Wave Equations by Using the Complete Discrimination System

2022

Mathematical Problems in Engineering

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First, our work is to transform the space-time fractional approximate long water wave equations into nonlinear ordinary differential equations via the traveling wave transformation in the sense of conformable fractional derivative. Second, we simplify the nonlinear ordinary differential equations into an ordinary differential equation with only one variable by integration and some transformations. Finally, we can further get all single traveling wave solutions of the space-time fractional approximate long water wave equations by the complete discrimination system for the four-order polynomial method; these solutions include the hyperbolic function solutions, rational function solutions, and implicit solutions.

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“…e nonlinear Schrödinger equation (NLSE) is usually used to describe many problems in nonlinear optics, quantum mechanics, fluid dynamics, plasmas, and so on [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Classification of All Single Traveling Wave Solutions of Fractional Perturbed Gerdjikov–Ivanov Equation

Han

2021

Mathematical Problems in Engineering

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The fractional perturbed Gerdjikov–Ivanov (pGI) equation plays a momentous role in nonlinear fiber optics, especially in the application of photonic crystal fibers. Constructing traveling wave solutions to this equation is a very challenging task in physics and mathematics. In the current article, our main purpose is to give the classifications of traveling wave solutions of the fractional pGI equation. These results can help physicists to further explain the complex fractional pGI equation.

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Bifurcation and new exact traveling wave solutions to time-space coupled fractional nonlinear Schrödinger equation

Cited by 55 publications

References 30 publications

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

New Classifications of All Single Traveling Wave Solutions of the Fractional Approximate Long Water Wave Equations by Using the Complete Discrimination System

Classification of All Single Traveling Wave Solutions of Fractional Perturbed Gerdjikov–Ivanov Equation

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