相关论文: Mode stability of self-similar wave maps in higher…

Given different speeds $c_1$ , ... , $c_K$, in the present paper we establish the existence of a solution to the Zakharov system in dimension 1 that behaves asymptotically like a $K$-solitary wave, each wave travelling with speed $c_k$. The…

Detection of bending waves is a highly challenging task even in nearby disc galaxies due to their sub-kpc bending amplitudes. However, simulations show that the harmonic bending of a Milky Way like disc galaxy is associated with a harmonic…

We are concerned with the radially symmetric stationary wave for the exterior problem of two-dimensional Burgers equation. A sufficient and necessary condition to guarantee the existence of such a stationary wave is given and it is also…

We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave maps equation we use a…

We study the transverse spectral stability of the one-dimensional small-amplitude periodic traveling wave solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky (KD) equation. We show that these waves are transversely unstable with…

The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…

In Euclidean space, the generalised Minkowski problem asks, for a given finite Radon measure $\mu$ on the unit sphere $\mathbb{S}^d$, to find a compact convex set $K$ with area measure $\mu$. For convex sets in the Minkowski space invariant…

We consider equivariant wave maps from a wormhole spacetime into the three-sphere. This toy-model is designed for gaining insight into the dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture. We first prove…

This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive…

In this note we derive an upper bound for the Hausdorff dimension of the stable set of a hyperbolic set $\Lambda$ of a $C^2$ diffeomorphisms on a $n$-dimensional manifold. As a consequence we obtain that $\dim_H W^s(\Lambda)=n$ is…

This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or…

We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.

The origin of our four-dimensional space-time has been pursued through the dynamical aspects of the IIB matrix model via the improved mean field approximation. Former works have been focused on the specific choice of configurations as…

We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…

We derive quantitative stability results for Minkowski bodies, as well as their counterparts, the $L_p$-Minkowski bodies in the range $1 \le p \neq n$. We prove that, for every pair of probability measures $\mu,\nu$ satisfying a…

An example of a toy model of $D=2$ Minkowski space and Poincar\'e group with real deformation parameter $q$ is considered. A notion of free motion is defined. The kinematics and phase-space are constructed and the ``uncertainity'' ralations…

In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact…

We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…

This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group $S_n$ on the cohomology of the configuration space of $n$ ordered points in $\mathbf{R}^d$. This cohomology is known to…