Stability analysis of embedded solitons in the generalized third-order nonlinear Schrödinger equation

2005 ◽  
Vol 15 (3) ◽  
pp. 037115 ◽  
Author(s):  
Dmitry E. Pelinovsky ◽  
Jianke Yang
Keyword(s):  
Stability Analysis ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Third Order ◽  
Nonlinear Schrödinger

Stability analysis, solitary wave and explicit power series solutions of a (2 + 1)-dimensional nonlinear Schrödinger equation in a multicomponent plasma

2021 ◽  
Vol 31 (5) ◽  
pp. 1732-1748
Author(s):  
Shou-Fu Tian ◽  
Xiao-Fei Wang ◽  
Tian-Tian Zhang ◽  
Wang-Hua Qiu
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Solitary Wave Solutions ◽  
Content Type ◽  
Nonlinear Schrödinger ◽  
Multicomponent Plasma

Purpose The purpose of this paper is to study the stability analysis and optical solitary wave solutions of a (2 + 1)-dimensional nonlinear Schrödinger equation, which are derived from a multicomponent plasma with nonextensive distribution. Design Methodology Approach Based on the ansatz and sub-equation theories, the authors use a direct method to find stability analysis and optical solitary wave solutions of the (2 + 1)-dimensional equation. Findings By considering the ansatz method, the authors successfully construct the bright and dark soliton solutions of the equation. The sub-equation method is also extended to find its complexitons solutions. Moreover, the explicit power series solution is also derived with its convergence analysis. Finally, the influences of each parameter on these solutions are discussed via graphical analysis. Originality Value The dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional nonlinear Schrödinger equation type nonlinear wave fields.

On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients

2015 ◽  
Vol 17 (04) ◽  
pp. 1450031 ◽  
Author(s):  
Xavier Carvajal ◽  
Mahendra Panthee ◽  
Marcia Scialom
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scaling Limit ◽  
Nonlinear Schrodinger Equation ◽  
Time Dependent ◽  
Well Posedness ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
The Third

We consider the Cauchy problem associated to the third-order nonlinear Schrödinger equation with time-dependent coefficients. Depending on the nature of the coefficients, we prove local as well as global well-posedness results for given data in L2-based Sobolev spaces. We also address the scaling limit to fast dispersion management and prove that it converges in H1to the solution of the averaged equation.

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