Related papers: Generalized Landau-Lifshitz Equation into $S^n$
In this paper, we study an inhomogeneous variant of the normalized $p$-Laplacian evolution which has been recently treated in \cite{BG1}, \cite{Do}, \cite{MPR} and \cite{Ju}. We show that if the initial datum satisfies the pointwise…
In this paper, we investigate the chiral boundary value problem for the Landau-Lifshitz equation with helical derivatives. By introducing Sobolev spaces adapted to the helical derivative and establishing energy estimates that are compatible…
The local and global existence of the Cauchy problem for semilinear heat equations with small data is studied in the weighted $L^\infty (\mathbb R^n)$ framework by a simple contraction argument. The contraction argument is based on a…
We construct new higher-order implicit-explicit (IMEX) schemes using the generalized scalar auxiliary variable (GSAV) approach for the Landau-Lifshitz equation. These schemes are linear, length preserving and only require solving one…
We study the Cauchy problem for the cubic nonlinear Schroedinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we…
We propose a generalization of Schramm-Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
The post-Newtonian approximation of general relativistic Liouville's equation is presented. Two integrals of it, generalizations of the classical energy and angular momentum, are obtained. Polytropic models are constructed as an…
The article consider an interpretation of Majorana equations as a quantum Lorentz covariant equations for the field of Einstein photon. A photon with "deinterlaced" spins (with diagonal Hamiltonian) is considered, its generalized Green…
Applying logarithmic transformations along 2-tori, we construct a generalized complex structure J_n with n type changing luci for every $n\geq 0$ on genus 1-Lefschetz fibrations with a cusp neighborhood, which include elliptic surfaces with…
We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement…
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in Besov spaces. Our estimates generalize the estimates…
In this paper, we establish local well-posedness of the Cauchy problem for a recently proposed dispersion generalized Camassa-Holm equation by using Kato's semigroup approach for quasi-linear evolution equations. We show that for initial…
In the recent works \cite{Cannarsa-Chen-Cheng} and \cite{Cannarsa-Cheng3}, an intrinsic approach of the propagation of singularities along the generalized characteristics was obtained, even in global case, by a procedure of sup-convolution…
The Jackiw-Teitelboim gauge formulation of the 1+1 dimensional gravity allows us to relate different gauge fixing conditions with integrable hierarchies of evolution equations. We show that the equations for the Zweibein fields can be…
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…
In this paper we study a generalized Cahn-Hilliard equation which was proposed by Gurtin. We prove the existence and uniqueness of a local-in-time solution for a quasilinear version, that is, if the coefficients depend on the solution and…
We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great…
In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove $L^p-L^q$ estimates for the solutions…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…