Related papers: Diffusive stability of spatially periodic patterns…
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regularity initial data $L^2({\mathbb T})\times L^2({\mathbb T})$…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
We carry out a stability analysis for the real space split operator method for the propagation of the time-dependent Klein-Gordon equation that has been proposed Ruf et al. [M. Ruf, H. Bauke, C.H. Keitel, A real space split operator method…
The complex Ginzburg--Landau equation serves as a paradigm of pattern formation and the existence and stability properties of Ginzburg--Landau $m$-armed spiral waves have been investigated extensively. However, many multi-armed spiral waves…
We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider…
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…
We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show that for a mixture of spherical Gaussian $P$ (sGMM) in a…
Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…
The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of…
Motivated by the problem of robustness to deformations of the input for deep convolutional neural networks, we identify signal classes which are inherently stable to irregular deformations induced by distortion fields $\tau\in…
We consider a coupled Wave-Klein-Gordon system in 3D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch-Ma as a simplified…
This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
We study a complex Ginzburg-Landau (GL) type model related to fluid instabilities in the boundary of magnetized toroidal plasmas (called edge-localized modes) with a prescribed shear flow on the Neumann boundary condition. We obtain the…
We generalize work of Oh & Zumbrun and Serre on spectral stability of spatially periodic traveling waves of systems of viscous conservation laws from the one-dimensional to the multi-dimensional setting. Specifically, we extend to…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
We study the stability of Hopfions embedded in a certain modification Ginzburg-Landau model of two equally charged condensates. It has been shown by Ward [Phys. Rev. D66, 041701(R) (2002)] that certain modification of the ordinary model…
Zeitlin's model is a discretisation of the 2-D Euler equations that preserves the underlying geometric structure. This feature makes it suitable for studying the qualitative behaviour of the dynamics. Here, we utilise Arnold's geometric…
We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…