26 citations · 53 across the 12 of their papers we have counts for
13 papers
Numerical study of a nonlocal nonlinear Schrödinger equation (MMT model)
Amin Esfahani, Gulcin M. Muslu
In this paper, we study a nonlocal nonlinear Schrödinger equation (MMT model). We investigate the effect of the nonlocal operator appearing in the nonlinearity on the long-term beh…
On the orbital stability of solitary waves for the fourth order nonlinear Schrödinger equation
Handan Borluk, Gulcin M. Muslu, Fábio Natali
In this paper, we present new results regarding the orbital stability of solitary standing waves for the general fourth-order Schrödinger equation with mixed dispersion. The existe…
Stability of Periodic Waves for the Defocusing Fractional Cubic Nonlinear Schrödinger Equation
Handan Borluk, Gulcin M. Muslu, Fábio Natali
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schrödinger equation. Our approach is based on periodic per…
Long time behavior of solutions to the generalized Boussinesq equation
Amin Esfahani, Gulcin M. Muslu
In this paper, we study the generalized Boussinesq equation as a model for the water wave problem with surface tension. Initially, we investigate the initial value problem within S…
Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrodinger equation
Gabriel E. Bittencourt Moraes, Handan Borluk, Guilherme de Loreno +2
In this paper, the existence and orbital stability of the periodic standing waves solutions for the nonlinear fractional Schrodinger (fNLS) equation with cubic nonlinearity is stud…
On the Kadomtsev-Petviashvili equation with double-power nonlinearities
Amin Esfahani, Steven Levandosky, Gulcin M. Muslu
In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the exist…
On the Rosenau equation: Lie symmetries, periodic solutions and solitary wave dynamics
Ali Demirci, Yasin Hasanoglu, Gulcin M. Muslu +1
In this paper, we first consider the Rosenau equation with the quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of the equation to ODEs, and find…
On the Stability of Solitary Wave Solutions for a Generalized Fractional Benjamin-Bona-Mahony Equation
Goksu Oruc, Fábio Natali, Handan Borluk +1
In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin-Bona-Mahony type equation. Besides the well kno…
On the existence, uniqueness and stability of Periodic Waves for the fractional Benjamin-Bona-Mahony equation
Sabrina Amaral, Handan Borluk, Gulcin M. Muslu +2
The existence, uniqueness and stability of periodic traveling waves for the fractional Benjamin-Bona-Mahony equation is considered. In our approach, we give sufficient conditions t…
The Generalized Fractional Benjamin-Bona-Mahony Equation: Analytical and Numerical Results
Goksu Oruc, Handan Borluk, Gulcin M. Muslu
The generalized fractional Benjamin-Bona-Mahony (gfBBM) equation models the propagation of small amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium.…
Numerical solution for a general class of nonlocal nonlinear wave equations
Handan Borluk, Gulcin M. Muslu
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel functio…
Higher order dispersive effects in regularized Boussinesq equation
Goksu Topkarci, Handan Borluk, Gulcin M. Muslu
In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation co…
The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model
H. A. Erbay, A. Erkip, G. M. Muslu
This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-…