Related papers: Slow Blow Up in the (2+1)-dimensional S^2 Sigma Mo…
The goal of this paper is to study the behavior of certain solutions to the Swift-Hohenberg equation on a one-dimensional torus $\mathbb{T}$. Combining results from $\Gamma$-convergence and ODE theory, it is shown that solutions…
The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…
Soft-collinear effective theory (SCET) is used to sum Sudakov double-logarithms in the x ->1 endpoint region for the deep inelastic scattering structure function. The calculations are done in both the target rest frame and the Breit frame.…
The usual cubic-quintic (CQ) nonlinearity is proved to sustain one- and two-dimensional (1D and 2D) broad (flat-top) solitons. In this work, we demonstrate that 1D and 2D soliton families can be supported, in the semi-infinite bandgap…
The soliton-like coherent structure (SCS), which has been verified to exist in both transitional and turbulent boundary layers1-4, still poses a challenge in the understanding of its formation and behavior. In our previous study (Niu et…
We show that $S^2\times S^2$ is isolated as a shrinking Ricci soliton in the space of metrics, up to scaling and diffeomorphism. We also prove the same rigidity for $S^2\times N$, where $N$ belongs to a certain class of closed Einstein…
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions.…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We consider the energy critical four dimensional semi linear heat equation \partial tu-\Deltau-u3 = 0. We show the existence of type II finite time blow up solutions and give a sharp description of the corresponding singularity formation.…
In this work, we review two methods used to approach singular Hamiltonians in (2+1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially…
Two-dimensional sigma models on superspheres $S^{r-1|2s} \cong OSp(r|2s)/OSp(r - 1|2s)$ are known to flow to weak coupling $g_{\sigma} \to 0$ in the IR when $r - 2s < 2$. Their long-distance properties are described by a free 'Goldstone'…
In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data…
The dynamics of bubble solitons in two-dimensional isotropic antiferromagnets, inhomogeneously doped so that the exchange integral J becomes position dependent, is studied. In the usual continuum approximation, the system reduces to a…
Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the $d$-dimensional sphere to itself for $3\leq d\leq 6$. By gluing together shrinking and…
The focusing cubic nonlinear Schr\"odinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Qm(r,theta) = e^{i m theta} Rm(r). In the case of spin m = 1, we prove there exists a class of…
In the theory of optical gap solitons, slowly-moving finite-amplitude Lorentzian solutions are found to mediate the transition from bright to coexistent dark-antidark solitary wave pairs when the laser frequency is detuned out of the proper…
A finite-time singularity of 2D harmonic map flow will be called "strictly type-II" if the outer energy scale satisfies $\lambda(t) = O(T - t)^{\frac{1 + \alpha}{2}}.$ We prove that the body map at a strict type-II blowup is H\"older…
We introduce two- and one-dimensional (2D and 1D) systems of two linearly-coupled Gross-Pitaevskii equations (GPEs) with the cubic self-attraction and harmonic-oscillator (HO) trapping potential in each GPE. The system models a…
A numerical study of low-lying glueball masses of compact U(1) lattice gauge theory in (2+1) dimensions is performed using Standard Path integral Monte Carlo techniques. The masses are extracted, at fixed (low) temperature, from simulations…
We consider the focusing nonlinear Schr\"odinger equations $i\partial_t u+\Delta u +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities $p_c<p<(1+\e)p_c$ with $p_c=1+\frac{4}{N}$ and $0<\e\ll 1$.…