Related papers: The Swift-Hohenberg equation with a nonlocal nonli…
The stability of a circular localized spot with respect to azimuthal perturbations is studied in in a variational Swift-Hohenberg model equation. The conditions under which the circular shape undergoes an elliptical deformation that…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
The paper is dedicated to a system of matrix nonlinear evolution equations related to a Hermitian symmetric space of the type $\mathbf{A.III}$. The system under consideration extends the $1+1$ dimensional Heisenberg ferromagnet equation in…
In previous works we analysed conditions for linearization of hermitian kernels. The conditions on the kernel turned out to be of a type considered previously by L. Schwartz in the related matter of characterizing the real space generated…
In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on the pattern. As such model we consider an anisotropic Swift-Hohenberg equation adding an additive noise. We prove the…
We consider the EBT algorithm (a particle method) for the non-local equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel which is not Lipschitz continuous, thus preventing the…
We consider a broad class of nonlinear integro-differential equations with a kernel whose differentiability order is described by a general function $\phi$. This class includes not only the fractional $p$-Laplace equations, but also…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
We study the asymptotic behavior of solutions to a monostable integro-differential Fisher-KPP equation , that is where the standard Laplacian is replaced by a convolution term, when the dispersal kernel is fat-tailed. We focus on two…
Recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms one of which represents a trivial covariantization of the…
Entanglement is a central resource in quantum information science, yet its structure in high dimensions remains notoriously difficult to characterize. One of the few general results on high-dimensional entanglement is given by peel-off…
We consider the steady Swift - Hohenberg partial differential equation. It is a one-parameter family of PDE on the plane, modeling for example Rayleigh - B\'enard convection. For values of the parameter near its critical value, we look for…
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this…
Many related products and coproducts (e.g. Hadamard, Cauchy, Kronecker, induction, internal, external, Solomon, composition, Malvenuto-Reutenauer, convolution, etc.) have been defined in the following objects : species, representations of…
A non-separable wave-like integro-differential equation for the time evolution of the Wigner distribution function in phase space is educed from the corresponding separable kinetic equation. It is shown that it leads to non-local dispersion…
The discrete Frenet equation entails a local framing of a discrete, piecewise linear polygonal chain in terms of its bond and torsion angles. In particular, the tangent vector of a segment is akin the classical O(3) spin variable. Thus…
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…
We extend and apply a recently developed approach to the study of dynamic bifurcations in PDEs based on the geometric blow-up method. We show that this approach, which has so far only been applied to study a dynamic Turing bifurcation in a…
The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a…
In \cite{christlieb2019kernel}, the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take the form of an explicit scheme. This paper extends such…