Related papers: The principal eigenvalue problem for time-periodic…
In (1+1)-dimensional quantum field theory, integrability is typically defined as the existence of an infinite number of local charges of different Lorentz spin, which commute with the Hamiltonian. A well known consequence of integrability…
In this paper, we focus on the nonlocal dispersal monostable equation with seasonal succession, which can be used to describe the dynamics of species in an environment alternating between bad and good seasons. We first prove the existence…
This article deals with the existence and non-existence of positive solutions for the eigenvalue problem driven by nonhomogeneous fractional $p\& q$ Laplacian operator with indefinite weights $$\left(-\Delta_p\right)^{\alpha}u +…
Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians,…
In this paper we provide a version of the Floquet's theorem to be applied to any second order difference equations with quasi-periodic coefficients. To do this we extend to second order linear difference equations with quasi-periodic…
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal…
In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive that the solution is positive when the source term is nonpositive by a subordination principle for the solution. As an…
Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a…
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For…
In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the…
In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the…
We develop a theoretical framework that lays out the fundamental rules under which a periodic (Floquet) driving scheme can induce non-reciprocal transport. Our approach utilizes an extended Hilbert space where a Floquet network with an…
We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in Fokas & Lenells 2012 for nonlinear…
We consider a class of nonlinear integro-differential operators and prove existence of two principal (half) eigenvalues in bounded smooth domains with exterior Dirichlet condition. We then establish simplicity of the principal…
A diffusion's induced transport is defined for a linear model of a Fokker-Plank equation under periodic boundary conditions in one-dimensional geometry. The flow is generated by a diffusion and a periodic deriving force induced by a…
At the moment, the most efficient method to compute the state of a periodically driven quantum system is using Floquet theory and the Floquet eigenbasis. The wide application of this basis set method is limited by: a lack of unique ordering…
In this short note we discuss the influence of a time-periodic dissipation term on a-priori estimates for solutions to dissipative wave equations. The approach is based on a diagonalisation argument for high frequencies and results from…