Related papers: Finding Eigenvalues the Rupert Way
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
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…
In this paper we analyze the stability of the traveling wave solution for an ignition-temperature, first-order reaction model of thermo-diffusive combustion, in the case of high Lewis numbers (${\rm Le} >1$). The system of two parabolic…
In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrodinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of…
When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of…
We present a new computational method for the accurate identification of the propagation modes and polarizations of elastic waves propagating in periodic solid structures and metamaterials. The method uses the eigenvectors calculated at…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < $\alpha$ < 1. We turn the free interface problem…
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
The numerical hydrodynamic modelling of beat Cepheid behavior has been a longstanding quest in which purely radiative models have failed miserably. We find that beat pulsations occur naturally when turbulent convection is accounted for in…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is…
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that…
An essential part of nondestructive testing and experimental modeling of waveguides is the decomposition of propagating wave patterns. The traveling wave ratio is a measure of partial reflections assisting in quantifying the pureness of a…
In this paper, we study the existence and stability of random transition waves for time heterogeneous Fisher-KPP Equations with nonlocal diffusion. More specifically, we consider general time heterogeneities both for the nonlocal diffusion…
We are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of…