Related papers: Scattering for NLS with a delta potential
Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a…
We prove the scattering for the defocusing generalized Benjamin-Ono equation in the energy space $H^{\frac{1}{2}}(\mathbb{R})$. We first establish the monotonicity formula that describes the unidirectional propagation. More precisely, it…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
We develop a theory for light scattering from a disordered layer of metal nanoparticles resting on a sample. Averaging over different disorder realizations is done by a coherent potential approximation. The calculational scheme takes into…
We study the inverse scattering problem for the three dimensional nonlinear Schroedinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of…
We consider the NLS with variable coefficients in dimension $n\ge3$ \begin{equation*} i \partial_t u - Lu +f(u)=0, \qquad Lv=\nabla^{b}\cdot(a(x)\nabla^{b}v)-c(x)v, \qquad \nabla^{b}=\nabla+ib(x), \end{equation*} on $\mathbb{R}^{n}$ or more…
The nonrelativistic full-folding optical model approach for nucleon-nucleus scattering is extended into the relativistic regime. In doing so, kinematical issues involving the off-shell Lorentz boost of the colliding particles between the…
The closed-form $T$ matrices in the $^3S_1$$-$$^3D_1$ channels of EFT($\not/!/!/pi$) for $NN$ scattering with the potentials truncated at order $\mathcal{O}(Q^4)$ are presented with the nonperturbative divergences parametrized in a general…
I criticize the claim, made in a recent article [C. M. Bender and L. R. Mead, Eur. J. Phys. 20, 117 (1999)], that in order to obtain the correct cross section for the scattering from a two-dimensional delta-function potential one must…
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second…
This manuscript proves the energy scattering of global solutions to a repulsive fourth-order generalized Hartree equation with non-radial data in the inter-critical regime. This work uses a new approach due to Dodson-Murphy [4] and extends…
We study the quantum scattering in two spatial dimensions (2D). Our computational scheme allows to quantitatively analyze the scattering parameters for the strong anisotropy of the interaction potential. High efficiency of the method is…
In this paper, we prove scattering asymptotics for the 2D (discrete dimension) cubic resonant system. This scattering result was used in Zhao \cite{Z1} as an assumption to obtain the scattering for cubic NLS on $\mathbb{R}^2\times…
We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing properties of the associated scattering operator and precise…
We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of…
In 2013 a new nonlocal symmetry reduction of the well-known AKNS scattering problem was found; it was shown to give rise to a new nonlocal $PT$ symmetric and integrable Hamiltonian nonlinear Schr\"{o}dinger (NLS) equation. Subsequently, the…
In this article we study the asymptotic behavior of a quadratic NLS equation with small, time-dependent potential and small spatially localized initial data. We prove global existence and scattering of solutions. The two main ingredients of…
In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…
We achieve unidirectional forward superscattering by multilayered spherical cavities which are effectively radially anisotropic. It is demonstrated that, relying on the large effective anisotropy, the electric and magnetic dipoles can be…
We investigate polarization observables in hyperon-nucleon scattering by decomposing scattering amplitudes into spin-space tensors, where each component describes scattering by corresponding spin-dependent interactions, so that…