THE NUMERICAL APPROXIMATION OF STATIONARY WAVE SOLUTIONS FOR TWO-COMPONENT SYSTEM OF NONLINEAR SCHRÖDINGER EQUATIONS BY USING GENERALIZATION PETVIASHVILI METHOD

Nuzla Af’Idatur Robbaniyyah; Jann Long Chern; Abdurahim

doi:10.30598/barekengvol18iss3pp1739-1752

THE NUMERICAL APPROXIMATION OF STATIONARY WAVE SOLUTIONS FOR TWO-COMPONENT SYSTEM OF NONLINEAR SCHRÖDINGER EQUATIONS BY USING GENERALIZATION PETVIASHVILI METHOD

Nuzla Af’Idatur Robbaniyyah, Jann Long Chern, Abdurahim^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The Petviashvili method is a numerical method for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: Mu + u^p = 0, where M is a positive definite and self-adjoint operator and p is constant. Due to the case being a system of solitary nonlinear wave equations, we generalize the Petviashvili method. We apply this generalized method for a two-component system of Nonlinear Schrödinger Equations (NLSE) for 2-D.

Original language	English
Pages (from-to)	1739-1752
Number of pages	14
Journal	Barekeng
Volume	18
Issue number	3
DOIs	https://doi.org/10.30598/barekengvol18iss3pp1739-1752
Publication status	Published - 2024 Mar 8

Keywords

Equations
Nonlinear Schrödinger
Petviashvili Method
Stationary wave Solutions

ASJC Scopus subject areas

Applied Mathematics
Statistics, Probability and Uncertainty
Mathematics (miscellaneous)
Numerical Analysis

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10.30598/barekengvol18iss3pp1739-1752

Cite this

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abstract = "The Petviashvili method is a numerical method for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: Mu + up = 0, where M is a positive definite and self-adjoint operator and p is constant. Due to the case being a system of solitary nonlinear wave equations, we generalize the Petviashvili method. We apply this generalized method for a two-component system of Nonlinear Schr{\"o}dinger Equations (NLSE) for 2-D.",

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AB - The Petviashvili method is a numerical method for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: Mu + up = 0, where M is a positive definite and self-adjoint operator and p is constant. Due to the case being a system of solitary nonlinear wave equations, we generalize the Petviashvili method. We apply this generalized method for a two-component system of Nonlinear Schrödinger Equations (NLSE) for 2-D.

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KW - Stationary wave Solutions

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THE NUMERICAL APPROXIMATION OF STATIONARY WAVE SOLUTIONS FOR TWO-COMPONENT SYSTEM OF NONLINEAR SCHRÖDINGER EQUATIONS BY USING GENERALIZATION PETVIASHVILI METHOD

Abstract

Keywords

ASJC Scopus subject areas

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