Related papers: Direct Scattering for the Benjamin-Ono Equation wi…
In this work, we consider the generalized variable-coefficient nonlinear Schr\"{o}dinger equation with non-vanishing boundary conditions at infinity including the simple and double poles of the scattering coefficients. By introducing an…
We study the direct and inverse scattering problems for the AKNS (Ablowitz-Kaup-Newell-Segur) system. New representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In…
Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A…
We present concise, computationally efficient formulas for several quantities of interest -- including absorbed and scattered power, optical force (radiation pressure), and torque -- in scattering calculations performed using the…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…
We study the scattering of solitons in the nonlinear Schroedinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The…
We perform quantitative spectral analysis on the Born equation, an integral equation for electromagnetic scattering that descends from the Maxwell equations. We establish norm bounds for the Green operator associated with the Born equation,…
Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
The $O(n)$ $\phi^4$ model on a strip bounded by a pair of planar free surfaces at separation $L$ can be solved exactly in the large-$n$ limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schr\"odinger…
A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…
We propose an inverse scattering transform for the continuum Calogero-Moser equation. We give a rigorous treatment of the direct scattering problem by constructing the associated Jost solutions and introducing a distorted Fourier transform,…
We identify the zero dispersion limit of a solution of the Benjamin--Ono equation on the line corresponding to every initial datum in $L^2(\R)\cap L^\infty(\R )$. We infer a maximum principle and a local smoothing property for this limit.…
We develop a simple tensorial contraction method to obtain analytical formula for X-ray resonant magnetic scattering. We apply the method considering first electric dipole-dipole and electric quadrupole-quadrupole scattering in the isolated…
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^2(\mathbb{R})$ is obtained explicitly for generic rational initial data $u_0$. An explicit asymptotic wave profile…
A spectral analysis is done on the $L$ operator of the Lax pair for the Benjamin-Ono equation. Simplicity and finiteness of the discrete spectrum are established as are needed for the Fokas and Ablowitz inverse scattering transform scheme.…
We consider the generalized Benjamin-Ono (gBO) equation on the real line, $ u_t + \partial_x (-\mathcal H u_{x} + \tfrac1{m} u^m) = 0, x \in \mathbb R, m = 2,3,4,5$, and perform numerical study of its solutions. We first compute the ground…
We investigate the dynamics of matter and optical waves at the early stage of superradiant Rayleigh scattering from Bose-Einstein Condensates. Our analysis is within a spatially dependent quantum model which is capable of providing analytic…