Stability analysis and soliton solutions for unstable nonlinear Schrodinger equation via two potential methods

Articles in Press

Document Type : Research Paper

Authors

1 1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. 2. Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan.

2 University of Al-Ameed, Karbala, Iraq.

3 Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan.

Abstract

This paper presents the analytical techniques to investigate the unstable
nonlinear Schrodinger equation (NLSE). The exact solutions to the unstable NLSE
which are found based on the generalized extended trial equation scheme and the improved
Bernoulli sub-ODE scheme (IBSOS) with three cases, by utilizing Maple software.
A system of nonlinear algebra differential equations is obtained, afterwards, this
system by help of Maple is solved. The discovered solutions include hyperbolic function,
trigonometric function, exponential, and rational solutions. Plenty of such types
nonlinear equations arising in basic fabric of communications network technology and
nonlinear optics which are investigated via mentioned methods. It offers theoretical
application value for the study of complex wave dynamics in various scientific domains,
such as plasma physics, and nonlinear optics. Firstly, the wave transform converts the
considered model into a system of ordinary differential equations. Then, novel exact
solitary wave solutions are developed as periodic, dark, combined hyperbolic, and rational
functions. Specific parameter values help demonstrate the dynamic nature of
the constructed solutions through their implementation. In addition, the stability of
generated solitary wave solution through the Hamiltonian technique is investigated.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 10 July 2026

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History

  • Receive Date: 06 October 2025
  • Revise Date: 15 May 2026
  • Accept Date: 07 July 2026

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