In this paper, a generalized nonlinear Schrödinger-type equation with higher-order nonlocal nonlinearities and
Kudryashov’s arbitrary refractive index is studied. A wide range of physical phenomena, such as nonlinear optics, plasma dynamics,
and wave propagation in dispersive media, are modeled by this equation. By applying a traveling wave transformation, the system is
reduced to a singular planar dynamical system, which is subsequently regularized to facilitate a comprehensive bifurcation analysis.
The equilibrium points are classified based on system parameters, and corresponding phase portraits are constructed to illustrate
the qualitative dynamics across various bifurcation scenarios. The unified Riccati equation expansion method and the sine-Gordon
expansion method are used to obtain explicit analytical soliton solutions, which are expressed in trigonometric and hyperbolic forms
and capture a range of wave structures with different physical properties. Graphic representations in 2D and 3D are presented to
illustrate the propagation dynamics. The results contribute to the current solution landscape of nonlocal nonlinear systems and
provide new information on the Hamiltonian structure and bifurcation behavior of such singular wave models. To the best of our
knowledge, the dynamical classification and exact solutions presented here are new and have not been published before.
2025-09
The European Physical Journal Plus
(القضية : 912)
(الحجم : 140)
Optical solutions and bifurcations of Kudryashov’s arbitrary refractive index along with generalized nonlocal nonlinearities
In this paper, a generalized nonlinear Schrödinger-type equation with higher-order nonlocal nonlinearities and
Kudryashov’s arbitrary refractive index is studied. A wide range of physical phenomena, such as nonlinear optics, plasma dynamics,
and wave propagation in dispersive media, are modeled by this equation. By applying a traveling wave transformation, the system is
reduced to a singular planar dynamical system, which is subsequently regularized to facilitate a comprehensive bifurcation analysis.
The equilibrium points are classified based on system parameters, and corresponding phase portraits are constructed to illustrate
the qualitative dynamics across various bifurcation scenarios. The unified Riccati equation expansion method and the sine-Gordon
expansion method are used to obtain explicit analytical soliton solutions, which are expressed in trigonometric and hyperbolic forms
and capture a range of wave structures with different physical properties. Graphic representations in 2D and 3D are presented to
illustrate the propagation dynamics. The results contribute to the current solution landscape of nonlocal nonlinear systems and
provide new information on the Hamiltonian structure and bifurcation behavior of such singular wave models. To the best of our
knowledge, the dynamical classification and exact solutions presented here are new and have not been published before.
2025-09
Nonlinear Dynamics
(القضية : 11)
(الحجم : 113)
Bifurcation and exact optical solutions in weakly nonlocal media with cubic-quintic nonlinearity
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
(القضية : 3)
(الحجم : 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
(الحجم : 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
(الحجم : 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
الاطاريح
2020-07-15
sturm liouville eigenvalue problem
M.Sc Thesis in Applied Mathematics
2020
المؤتمرات العلمية
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].
الدورات التدريبية
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
