In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semistrong regime of two-pulse interactions in a regularized Gierer–Meinhardt system. In the semistrong limit the localized activator pulses interact strongly through the slowly varying inhibitor. The interaction is not tail-tail as in the weak interaction limit, and the pulse amplitudes and speeds ...

Recursion operators of partial diierential equations are identiied with BB acklund auto-transformations of linearized diieties. Relations to the classical concept and its recent Guthrie's generalization are discussed. Traditionally,a recursion operator of a PDE is a linear operator L acting on symmetries: if f is a symmetry then so is Lf. This provides a convenient way to generate innnite famil...

The linearized Vlasov equation for a plasma system in an external constant magnetic field and the corresponding linear Vlasov operator are studied. The solution of the Vlasov equation is found by the resolvent method. The spectrum and eigenfunctions of the Vlasov operator are also found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and c...

We study general semilinear scalar-field equations on the real line with variable coefficients in linear terms. These are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. motivated by question how these equation may change stability properties kink solutions (one-dimensional topological solitons). prove existence stationary solution our setting, and perfor...

Abstract It has been revealed that the first-order symmetry operator for linearized Einstein equation on a vacuum spacetime can be constructed from Killing–Yano 3-form. This might used to construct all or part of solutions field equation. In this paper, we perform mode decomposition metric perturbation Schwarzschild and Myers–Perry with equal angular momenta in 5 dimensions, investigate action ...

We present a deviational Monte Carlo method for solving the Boltzmann equation for phonon transport subject to the linearized ab initio 3-phonon scattering operator. Phonon dispersion relations and transition rates are obtained from density functional theory calculations. The ab initio scattering operator replaces the commonly used relaxation-time approximation, which is known to neglect, among...

The unique solvability in the sense of classical solutions for nonlinear inverse problems to differential equations, solved oldest Dzhrbashyan–Nersesyan fractional derivative, is studied. linear part equation contains a bounded operator, continuous operator that depends on lower-order derivatives, and an unknown element. problem given by equation, special initial value conditions lower overdete...

Analysis of stability under linearized dynamics is central to ecology. We highlight two key limitations of the widely used traditional analysis. First, we note that while stability at fixed points is often the focus, ecological systems may spend less time near fixed points, and more time responding to stochastic environmental forcing by exhibiting wide zero-mean fluctuations about those states....

We consider the asymptotic stability of transition front solutions for Cahn–Hilliard systems on R. Such equations arise naturally in the study of phase separation, and systems describe cases in which three or more phases are possible. When a Cahn–Hilliard system is linearized about a transition front solution, the linearized operator has an eigenvalue at 0 (due to shift invariance), which is no...