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The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA…
By means of an original approach, called "method of the moving frame", we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent…
We propose a more realistic version of the recently introduced split-step model (SSM), which consists of periodically alternating dispersive and nonlinear segments, by adding uniformly distributed loss and lumped gain to it. In the case…
In the present work the second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane limiting half-space makes harmonious fluctuations with variable amplitude in the plane. The amplitude changes on the…
In the present work we study discrete nonlinear Schr{\"o}dinger models combining nearest (NN) and next-nearest (NNN) neighbor interactions, motivated by experiments in waveguide arrays. While we consider the more experimentally accessible…
The asymptotic error distribution of numerical methods applied to stochastic ordinary differential equations has been well studied, which characterizes the evolution pattern of the error distribution in the small step-size regime. It is…
We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the…
In the present work, we consider the existence and spectral stability of multi-pulse solutions in Hamiltonian lattice systems. We provide a general framework for the study of such wave patterns based on a discrete analogue of Lin's method,…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
This study deals with an existing mathematical model of asymmetrically interacting agents. We analyze the following two previously unfocused features of the model: (i) synchronization of growth rates and (ii) initial value dependence of…
We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
This paper investigates the dynamic stability of an electromagnetically suspended vehicle, encountered in Hyperloop and Maglev systems, subject to periodic excitations caused by surface irregularities or vibration of the support induced by…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated…
We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a…
A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse…
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its…