In this study, we explore the bifurcation and optical soliton solutions in weakly nonlocal media with cubic-quintic nonlinearity, which are significant for understanding optical soliton propagation in nonlocal nonlinear systems. The cubic-quintic nonlinear Schrödinger equation, including weak nonlocality, is introduced to model the evolution of soliton trains in optical fibers under the influence of a nonlocal medium. Using a traveling wave transformation, the equation
is reduced to a singular dynamical system and further transformed into a regular dynamical system through changing variables. The study confirms the equivalence of the first integrals for both systems and provides a detailed analysis of phase portraits, emphasizing their geometric and topological features. Additionally, the unified Riccati equation expansion method is applied to derive exact solutions, including periodic, dark, and singular soliton solutions. 2D and 3D graphical representations of the solutions are presented to illustrate their physical properties, with parameters chosen to highlight the effects of cubic-quintic nonlinearity and weak nonlocality. These findings offer insights into the dynamics of nonlinear wave propagation in optical systems and contribute to advancements in nonlocal nonlinear optics and soliton theory.
2025-05
Turkish Journal of Computer and Mathematics Education
(Issue : 3)
(Volume : 13)
Periodic Solution for Nonlinear Second Order Differential Equation System
In this work, we investigate the periodic solutions for non-linear system of differential equations
by using the method of periodic solutions of ordinary differential equations which are given by
A.M.Samoilenko. Additionally, the existence and uniqueness theorem have been proved for second
differential equations system by using Banach fixed point theorem.
In this paper, we give a reconstruction formula for the potential q for a second order differential equation
with boundary condition which contains spectral parameter. For this as methodology, we use Prufer substitution ¨
that has an advantage different from other methods. Because in this method, we do not need any information of
eigenfunctions.
2021-08
CONTROL AND OPTIMIZATION WITH INDUSTRIAL APPLICATIONS
(Volume : 2)
DIFFERENCE BETWEEN THE TWO PERIODIC POTENTIALS ON THE INVERSE STURM-LIOUVILLE PROBLEM
Spectral analysis of the Sturm-Liouville operator with periodic potential has been examined in detail [1–4].
2020-08
CMES 2019, AISC
(Volume : 6)
Some novel solutions of the coupled Whitham-Broer-Kaup system
The shallow water equations have a wide range of applications in the ocean, atmospheric modeling, and pneumatic computing, which can also be used to modeling flows in rivers and coastal areas. In this study, we build the analytic traveling wave solution of the (1+1) dimensional coupled Whitham-Broer-Kaup (WBK) equations, by using the Bernoulli sub-equation function method. The system of (1+1)-dimensional (CWBK) partial differential equation is converted to the ordinary differential equation for obtaining new exponential prototype structures. We obtained new results using this technique. We plotted two and three-dimensional surfaces of the results using Wolfram Mathematica software. At the end of this study, we submitted a conclusion in a comprehensive manner.
2020-01
Thesis
2020-07-15
sturm liouville eigenvalue problem
M.Sc Thesis in Applied Mathematics
2020
Conference
The 7th International Conference on Control and Optimization with Industrial Applications
2020-08
DIFFERENCE BETWEEN THE TWO PERIODIC POTENTIALS ON THE INVERSE STURM-LIOUVILLE PROBLEM
Spectral analysis of the Sturm-Liouville operator with periodic potential has been examined in detail [1–4].
Training Course
2022-09-01,2022-10-14
Language Center
English Language Proficiency
2022
2022-06-07,2022-12-02
Pedagogical Training and Academic Development Center
Pedagogical Training
2022
2019-01-01,2019-07-01
Turkish language teaching application and research center
