Related papers: Long range scattering for the Maxwell-Schr"odinger…
We study the relationship between asymptotic characteristic initial data for the wave equation at past null infinity and the regularity of the solution at future null infinity on the Minkowski spacetime. By constructing estimates on a…
The Cauchy problem of the modified nonlinear Schr\"{o}dinger (mNLS) equation with the finite density type initial data is investigated via $\overline{\partial}$ steepest descent method. In the soliton region of space-time $x/t\in(5,7)$, the…
In this paper, we show that the Schr\"odinger-Bopp-Podolsky system with Dirichlet boundary conditions in a bounded domain possesses infinitely many solutions of prescribed frequency, for any set of (continuous) boundary conditions, provided…
In this paper, we study a coupled nonlinear Schr{\"o}dinger system with small initial data in the one dimension Euclidean space. Such a system appears in the context of the coupling between two different optical waveguides. We establish an…
We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schr\"odinger equation. Under generic assumptions on the initial value, the solution is asymptotically a sum of 1-solitons. We find different phase…
A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…
We consider the cubic nonlinear Schr\"{o}dinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initial value problem. Moreover, we also consider the failure…
We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
We discuss the formulation of the scattering asymptotic condition as a strong limit in Euclidean quantum theories satisfying the Osterwalder-Schrader axioms. When used with the invariance principle this provides a constructive method to…
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
We consider dispersive shock wave to the focusing nonlinear Schr\"odinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi-axis and zero on the right semi-axis. As an initial…
This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and…
We derive rigorously the non-linear macroscopic system associated to a microscopic system of coupled quintic Schr\"odinger equations in the framework of discrete wave turbulence under a particular scaling law that describes the limiting…
The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non self-adjoint scattering problem…