New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Xie, Yongan; Tang, Shengqiang

doi:10.1155/2014/826746

Cited by 7 publications

(4 citation statements)

References 10 publications

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“…e complete discriminant system method was first introduced by Lu and his collaborators in 1996 [16]. In recent years, many experts and scholars [17][18][19][20][21][22] have applied this method to construct the exact traveling wave solutions of partial differential equations. In this section, we intend to use this method to analyze the exact traveling wave solution of the variable-coefficient Davey-Stewartson system.…”

Section: Traveling Wave Solutions Of System (1)mentioning

confidence: 99%

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

Han

Wen

2022

Discrete Dynamics in Nature and Society

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This paper mainly studies the bifurcation and single traveling wave solutions of the variable-coefficient Davey–Stewartson system. By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. On the other hand, we use the polynomial complete discriminant method to obtain the exact traveling wave solution of the variable-coefficient Davey–Stewartson system.

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Section: Traveling Wave Solutions Of System (1)mentioning

confidence: 99%

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

Han

Wen

2022

Discrete Dynamics in Nature and Society

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“…Next, we can obtain the classification of solutions of (6) according to polynomial complete discrimination system (9) ( [18][19][20][21][22][23]).…”

Section: Preliminariesmentioning

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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“…This dependence leads to various particular nonlinear laws for the permittivity: cubic (Kerr), quintic, cubic-quintic, polynomial nonlinearities, power nonlinearity with noninteger degree, saturated nonlinearities, and so on. These nonlinearities were actively experimentally [4,5,[38][39][40][41][42][43][44][45][46] as well as theoretically [2,6,9,13,21,32,[35][36][37][47][48][49][50][51][52][53][54][55][56] studied.…”

Section: Statement Of the Problemmentioning

confidence: 99%

How Kerr nonlinearity influences polarized electromagnetic wave propagation

Валовик

2017

URSI Radio Sci. Bull.

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The propagation of electromagnetic TE waves along boundaries of a plane dielectric layer fi lled with a Kerr medium is studied for all possible cases of the problem's parameters. The layer is located between two half-spaces with constant permittivities. The problem is reduced to a nonlinear transmission eigenvalue problem for Maxwell's equations, in which each eigenvalue is a propagation constant of a guided wave. The exact dispersion equation with respect to the eigenvalues (propagation constants) is derived and studied. It is proven that in the presence of the Kerr eff ect, several novel wave-guiding regimes arise, including regimes that have no counterparts in the linear theory. An infi nite number of eigenvalues arise in the focusing case, even if the corresponding linear problem has no solutions (the linear problem always has no more than a fi nite number of solutions). In the defocusing case, only those solutions arise that tend to linear solutions when the nonlinearity coeffi cient vanishes. It is also proven that in the nonlinear case, an infi nite number of eigenvalues do not reduce to the solutions of the corresponding linear problem, even if the nonlinearity coeffi cient tends to zero. Numerical illustrations for the results obtained are provided.

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New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Cited by 7 publications

References 10 publications

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

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

How Kerr nonlinearity influences polarized electromagnetic wave propagation

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