Multidimensional Inverse Scattering for the Nonlinear Klein–Gordon Equation with a Potential
نویسندگان
چکیده
منابع مشابه
Inverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential
In the present work, under some di¤erentiability conditions on the potential functions , we rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...
متن کاملInverse Scattering for the Nonlinear Schrödinger Equation Ii. Reconstruction of the Potential and the Nonlinearity in the Multidimensional Case
We solve the inverse scattering problem for the nonlinear Schrödinger equation on Rn, n ≥ 3: i ∂ ∂t u(t, x) = −∆u(t, x) + V0(x)u(t, x) + ∞ ∑ j=1 Vj(x)|u|0u(t, x). We prove that the small-amplitude limit of the scattering operator uniquely determines Vj , j = 0, 1, · · · . Our proof gives a method for the reconstruction of the potentials Vj , j = 0, 1, · · · . The results of this paper extend ou...
متن کاملInverse scattering at high energies for the multidimensional Newton equation in a long range potential
We define scattering data for the Newton equation in a potential V ∈ C2(Rn,R), n ≥ 2, that decays at infinity like r−α for some α ∈ (0, 1]. We provide estimates on the scattering solutions and scattering data and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of the potential up to the knowledge of the long range tail of the potential....
متن کاملṕ Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential ∗
In this paper I prove a L − L estimate for the solutions of the one–dimensional Schrödinger equation with a potential in Lγ where in the generic case γ > 3/2 and in the exceptional case (i.e. when there is a half–bound state of zero energy) γ > 5/2. I use this estimate to construct the scattering operator for the nonlinear Schrödinger equation with a potential. I prove moreover, that the low–en...
متن کاملInverse Scattering for the Nonlinear Schrödinger Equation with the Yukawa Potential
We study the inverse scattering problem for the three dimensional nonlinear Schrödinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2002
ISSN: 0022-0396
DOI: 10.1006/jdeq.2001.4133