The Nonlinear Schrödinger Equation Derived from the Third Order Korteweg-de Vries Equation Using Multiple Scales Method

Authors

  • Murat Koparan Department of Mathematics and Science Education, Anadolu University Faculty of Education, Mathematics Education Division, Yunusemre Campus, 26470, Eskişehir, Turkey https://orcid.org/0000-0003-1698-9661

DOI:

https://doi.org/10.37256/cm.5420244647

Keywords:

perturbation, multiple scales method, third-order Korteweg-de Vries (KdV3) equation

Abstract

Nonlinear equations of evolution (NLEE) are mathematical models used in various branches of science. As a result, nonlinear equations of evolution have served as a language for formulating many engineering and scientific problems. For this reason, many different and effective techniques have been developed regarding nonlinear equations of evolution and solution methods. Although the origin of nonlinear equations of evolution dates back to ancient times, there have been significant developments regarding these equations from the past to the present. The main reason for this situation is that nonlinear equations of evolution involve the problem of nonlinear wave propagation. In recent years, equations of formation have become increasingly important in applied mathematics. This work focuses on the perturbation approach, often known as many scales, for nonlinear evolution equations. The article focuses on the analysis of the (1+1) dimensional third-order nonlinear Korteweg-de Vries (KdV) equation using the multiple scales method, which resulted in obtaining nonlinear Schrödinger (NLS) type equations.

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Published

2024-11-14

How to Cite

1.
Koparan M. The Nonlinear Schrödinger Equation Derived from the Third Order Korteweg-de Vries Equation Using Multiple Scales Method. Contemp. Math. [Internet]. 2024 Nov. 14 [cited 2024 Dec. 4];5(4):5087-9. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4647