Orumbayeva, Sara(Nazarbayev University, School of Science and Technology, 2019-08-07)
The Nonlinear Schrödinger equation (NLSE) is a prototypical example of nonlinear partial differential equation. It is commonly used to describe propagation of light in nonlinear optical fibers and is of great importance ...
Kazbek, Moldir(Nazarbayev University, School of Science and Technology, 2019-08-08)
Rogue waves are fascinating destructive phenomena in nature that have not been fully explained so far [1-3]. Oceanographers commonly agree that linear theories cannot provide explanations for their existence[6,7]. Only ...
Biyar, Magzhan(Nazarbayev University, School of Science and Technology, 2019-08-07)
We prove that the Cauchy problem for a transport equation with algebraic nonlinearity of
degree p with initial data in Gevrey spaces is locally well-posed. In particular, we show that
the analyticity of solutions persists ...
Kadenova, Aida(Nazarbayev University, School of Science and Technology, 2019-08-08)
The aim of this project is to analyze three different population models such as Gompertz, Logistic and Generalized Logistic based USA population data. Finding the appropriate model is essential in actuarial application. ...
Magzanov, Shynggys(Nazarbayev University, School of Science and Technology, 2019-08-08)
Credit risk modelling of a portfolio of exposures is essential part of activity of every financial institution. However this procedure is complicated since the joint behavior of chosen exposures must be known. In this paper ...
Yerlanov, Madi(Nazarbayev University, School of Science and Technology, 2019-08-07)
When one studies certain rings, it is natural to classify them according to certain properties. This project focuses on the study of properties of commutative rings associated with algebraic sets. In particular, we consider ...
We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with
gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there
exist finite-power, ...
We examine the role of long–range interactions on the dynamical and statistical properties of two
1D lattices with on–site potentials that are known to support discrete breathers: the Klein–Gordon
(KG) lattice which ...
Kominis, Yannis; Bountis, Tassos; Flach, Sergej(Physical Review A, 2017-06-21)
We analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations
in the presence of unbalanced gain and loss. At the parity-time (PT ) symmetry point the coupler is unstable.
Suitable ...
The fundamental active photonic dimer consisting of two coupled quantum well lasers is inves-
tigated in the context of the rate equation model. Spectral transition properties and exceptional
points are shown to occur ...
Bountis, Tassos; Vanhaecke, Pol(Physics Letters A, 2016-09)
We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These ...
An interesting problem in solid state physics is to compute discrete breather
solutions in N coupled 1–dimensional Hamiltonian particle chains and investigate
the richness of their interactions. One way to do this is to ...
Kominis, Yannis; Choquette, Kent D.; Bountis, Anastassios; Kovanis, Vassilios(arXiv, 2018-06)
We show the abundance of Exceptional Points in the generic asymmetric configuration of two
coupled diode lasers, under nonzero optical detuning and differential pumping. We pinpoint the
location of these points with ...
Coupled semiconductor lasers are systems possessing complex dynamics that are interesting for
numerous applications in photonics. In this work, we investigate the existence and the stability of
asymmetric phase-locked ...
Antonopoulos, Chris G.; Skokos, Charalampos; Bountis, Tassos; Flach, Sergej(arXiv, 2018-03-19)
In the study of subdiffusive wave-packet spreading in disordered Klein-
Gordon (KG) nonlinear lattices, a central open question is whether the
motion continues to be chaotic despite decreasing densities, or tends to
become ...
Rat, Sara(Nazarbayev University, School of Science and Technology, 2018)
The Financial Risk Management (FRM) aims to identify, measure and manage risks in different sectors. One of the core things during such operations is measuring different dependencies. Linear correlation is known as one of ...
A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic solutions and non-periodic solutions in the pull-in analysis of a graphene-based MEMS lumped parameter ...
In this Capstone Project, we analyze a second order nonlinear ordinary differential equation (NODE), y^" (x)=f(y^',y) that is impossible to solve analytically. First, using the Taylor Power Series method, we obtain a series ...
Kabdolov, Olzhas(Nazarbayev University, School of Science and Technology, 2018-05)
Recurrent neural networks are very powerful sequence models which are used for language modeling as well. Under correct regularization such as naive dropout these models are able to achieve substantial improvement in their ...
Shakir, Akyl(Nazarbayev University, School of Science and Technology, 2018-05)
We apply singularity analysis in complex time to investigate the solutions of a dynamical system of one degree of freedom related to the oscillations of a Micro-Electro-Mechanical System (MEMS) of nonlinear elasticity. ...