Related papers: Almost surely smoothed scattering for cubic NLS
We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schr\"odinger equations in two space dimensions for all powers $p>0$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in…
Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow quadratically with the wavenumber $k$. Here, we describe a solver which applies only when the scattering potential is…
We revisit a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schr\" odinger equation (NLS) with an attractive localized potential and a time-dependent factor in the nonlinearity. We show that, under generic hypotheses on…
In this work, we study some special properties of smoothness concerning to the initial value problem associated with the Zakharov-Kuznetsov-(ZK) equation in the $n-$ dimensional setting, $n\geq 2.$ It is known that the solutions of the ZK…
We consider the radial nonlinear Schr\"odinger equation $i\partial_tu +\Delta u = |u|^{p-1}u$ in dimension $d\geqslant 2$ for $p\in \left(1,1+\frac{4}{d}\right]$ and construct a natural Gaussian measure $\mu_0$ which support is almost…
This work investigates the long time asymptotic behavior of some inhomogeneous non-linear Schr\"odinger type equations. We give sharp a threshold of scattering versus non-scattering of mass solutions, depending on the source term. This work…
We consider the initial-value problem for the $1d$ cubic nonlinear Schr\"odinger equation with a repulsive delta potential. We prove that small initial data in a weighted Sobolev space lead to global solutions that decay in $L^\infty$ and…
Take two isomorphic convex co-compact co-infinite volume Kleinian groups, whose regular sets are diffeomorphic. The quotient of hyperbolic 3-space by these groups gives two hyperbolic 3-manifolds whose scattering operators may be compared.…
We study the two-dimensional periodic nonlinear Schr\"odinger equation (NLS) with the quadratic nonlinearity $|u|^2$. In particular, we study the quadratic NLS with random initial data distributed according to a fractional derivative (of…
We study the focusing intercritical NLS \begin{align}\label{abstract_nls} i\pt_t u+\Delta_{x,y}u=-|u|^\alpha u\tag{NLS} \end{align} on the semiperiodic waveguide manifold $\R^d_x\times \T_y$ with $d\geq 5$ and…
In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
In a previous work the authors described a fast high-fidelity computer model for acoustic scattering from multi-layered elastic spheres. This work is now extended with a scaling strategy significantly mitigating the problem of overflow and…
We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle,…
We present two new remarkably simple stochastic second-order methods for minimizing the average of a very large number of sufficiently smooth and strongly convex functions. The first is a stochastic variant of Newton's method (SN), and the…
This article is concerned with the small data problem for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global…
We prove large-data scattering in $H^1$ for inhomogeneous nonlinear Schr\"odinger equations in one space dimension for powers $p>2$. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the…