Inclusiveness Target Country Conference Grant

A Variety of Solutions of the Nonlinear Schrödinger Equation in a White Noise Environment

Esma Ulutas, Karadeniz Technical University, Trabzon, Turkey

The 3rd International Conference on Applied Mathematics in Engineering (ICAME’24)
Ayvalık - Balıkesir, Türkiye
26-28 June 2024

Grantee: Esma Ulutas, Karadeniz Technical University, Trabzon, Turkey
Type of publication: Abstract
Type of presentation: Oral

Start date: 2024-06-26
End date: 2024-06-28
Awarded: 2024-05-28
Report approved: 2024-08-29

Abstract

It is commonly known that the nonlinear Schrödinger equations (NLSE) are essential for comprehending a wide range of physical phenomena that arise in several scientific fields. It is also known that solving stochastic nonlinear partial differential equations (NPDEs) is more complex and challenging than deterministic equations due to additional random terms. In this study, it is considered Wick- type stochastic nonlinear Schrödinger equation with conformable derivatives. It is obtained a variety of solutions such as travelling wave and optical soliton solutions and also stochastic solutions using two powerful techniques. It is also used Hermite transforms and White noise theory to get these solutions. Additionally, it is demonstrated by two examples how the stochastic solutions can be written as Brownian motion functional solutions.

Publication

@inproceedings{Ulutas2024variety,
	address = {Bal\i{}kesir, T{\" u}rkiye},
	author = {Ulutas, Esma},
	booktitle = {The 3rd international conference on applied mathematics in engineering ({ICAME}\textquoteright{}24)},
	year = {2024},
	month = {6},
	pages = {52},
	title = {A variety of solutions of the nonlinear {Schr}{\" o}dinger equation in a white noise environment},
}