Related papers: Self trapping transition for a nonlinear impurity …
We study the nonlinear Schr\"odinger equation with a competing cubic-quintic power law nonlinearity on the waveguide domain $\mathbb R_x \times \mathbb T_{L_y}$. This model is globally well-posed and admits line solitary wave solutions,…
We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states.…
We consider a class of nonlinear Schrodinger equation in four and five space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2)…
We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…
As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open…
In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schr{\"{o}}dinger equation, we find discrete vortex solitons with various values of the topological charge $S$. Stability regions for the vortices with…
We provide an exact analytical solution of the single-particle Schr\"odinger equation for a chain of non-interacting fermions subject to a time-dependent linear potential, with its slope varied as an arbitrary function of time. The…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…
We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point…
A trapping-detrapping model is proposed for explaining the current fluctuation behavior in organic semiconductors (polyacenes) operating under current-injection conditions. The fraction of ionized traps obtained from the current-voltage…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
In these lectures, I review cosmological phase transitions and the topological aspects of spontaneous symmetry breaking. I then discuss the formation of walls, strings and monopoles during phase transitions including lattice based studies…
In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schr\"odinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions…
A numerical exploration of a gain-loss nonlinear Schr\"odinger equation was carried out utilizing over 180000 core hours to conduct more than 10000 unique simulations in an effort to characterize the model's six dimensional parameter space.…
We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model along with cubic Klein-Gordon type nonlinearity. We investigate the long-time dynamics of the nonlinear edge states, which are obtained by nonlinear continuation of…
In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, $(U(y),0)$, in a periodic channel under…
This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g. for infinite…
Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…