Inverse Scattering for the Nonlinear Schrödinger Equation with the Yukawa Potential
نویسندگان
چکیده
منابع مشابه
ṕ 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 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 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 کاملthe algorithm for solving the inverse numerical range problem
برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولThe Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential
The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground st...
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: Communications in Partial Differential Equations
سال: 2008
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300701790245