Ukrainian Journal of Physical Optics


2024 Volume 25, Issue 5


ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

CNOIDAL WAVES AND SOLITONS TO THREE-COUPLED NONLINEAR SCHRODINGER'S EQUATION WITH SPATIALLY-DEPENDENT COEFFICIENTS

Thilagarajah Mathanaranjan1, M.S. Mani Rajan2, S. Saravana Veni3 and Yakup Yildirim4,5

1Department of Mathematics and Statistics, University of Jaffna, Sri Lanka
2Department of Physics, Anna University, Madurai Region, Ramanathapuram, India
3Department of Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India
4Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
5Department of Mathematics, Near East University, 99138 Nicosia, Cyprus

ABSTRACT

This paper uses the extended auxiliary equation method to obtain the exact solutions of the nonlinear Schrödinger equations with variable-coefficient. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, and Jacobi elliptic functions solutions are obtained. The solitons are guaranteed to exist, provided the chromatic dispersion coefficients are Riemann integrable. Further, some of the obtained solutions are presented by 3D and 2D graphs to demonstrate the behavior of solutions. The results show that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding various exact solutions of nonlinear evolution equations with variable coefficients in mathematical physics.

Keywords: Nonlinear Schrodinger equations with variable coefficient, extended auxiliary equation method, optical soliton, elliptic functions solutions

UDC: 535.32

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    У цій статті використовується метод розширеного допоміжного рівняння для отримання точних розв’язків нелінійних рівнянь Шредінгера зі змінним коефіцієнтом. У результаті отримані розв’язки ізольованих хвиль, розв’язки тригонометричних функцій, розв’язки раціональних функцій та розв’язки еліптичних функцій Якобі. Солітони однозначно існують за умови, що коефіцієнти хроматичної дисперсії інтегровні за Ріманом. Крім того, деякі з отриманих рішень представлені 3D і 2D графіками, щоб продемонструвати поведінку рішень. Результати показують, що метод розширеного допоміжного рівняння за допомогою комп’ютерної системи символьних обчислень є надійним та ефективним у знаходженні різних точних розв’язків нелінійних еволюційних рівнянь зі змінними коефіцієнтами в математичній фізиці.

    Ключові слова: Nonlinear Schrodinger equations with variable coefficient, extended auxiliary equation method, optical soliton, elliptic functions solutions


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