ترغب بنشر مسار تعليمي؟ اضغط هنا

Inverse scattering for the nonlinear Schr{o}dinger equation with the Yukawa potential

171   0   0.0 ( 0 )
 نشر من قبل Hironobu Sasaki
 تاريخ النشر 2008
  مجال البحث
والبحث باللغة English
 تأليف Hironobu Sasaki




اسأل ChatGPT حول البحث

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 the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.



قيم البحث

اقرأ أيضاً

100 - Remi Carles 2021
We analyze dynamical properties of the logarithmic Schr{o}dinger equation under a quadratic potential. The sign of the nonlinearity is such that it is known that in the absence of external potential, every solution is dispersive, with a universal asy mptotic profile. The introduction of a harmonic potential generates solitary waves, corresponding to generalized Gaussons. We prove that they are orbitally stable, using an inequality related to relative entropy, which may be thought of as dual to the classical logarithmic Sobolev inequality. In the case of a partial confinement, we show a universal dispersive behavior for suitable marginals. For repulsive harmonic potentials, the dispersive rate is dictated by the potential, and no universal behavior must be expected.
In this paper, we study the existence and instability of standing waves with a prescribed $L^2$-norm for the fractional Schr{o}dinger equation begin{equation} ipartial_{t}psi=(-Delta)^{s}psi-f(psi), qquad (0.1)end{equation} where $0<s<1$, $f(psi)=|ps i|^{p}psi$ with $frac{4s}{N}<p<frac{4s}{N-2s}$ or $f(psi)=(|x|^{-gamma}ast|psi|^2)psi$ with $2s<gamma<min{N,4s}$. To this end, we look for normalized solutions of the associated stationary equation begin{equation} (-Delta)^s u+omega u-f(u)=0. qquad (0.2) end{equation} Firstly, by constructing a suitable submanifold of a $L^2$-sphere, we prove the existence of a normalized solution for (0.2) with least energy in the $L^2$-sphere, which corresponds to a normalized ground state standing wave of(0.1). Then, we show that each normalized ground state of (0.2) coincides a ground state of (0.2) in the usual sense. Finally, we obtain the sharp threshold of global existence and blow-up for (0.1). Moreover, we can use this sharp threshold to show that all normalized ground state standing waves are strongly unstable by blow-up.
The blowup is studied for the nonlinear Schr{o}dinger equation $iu_{t}+Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $pge 1+frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative energy $E(u_0)<0$ bl ows up in finite or infinite time. A new proof is also presented for the previous result in cite{HoRo2}, in which a similar result but more general in a case of energy-subcritical was shown.
98 - Jianjun Liu 2020
This paper is concerned with the derivative nonlinear Schr{o}dinger equation with periodic boundary conditions. We obtain complete Birkhoff normal form of order six. As an application, the long time stability for solutions of small amplitude is proved.
199 - Baoxiang Wang , Yuzhao Wang 2009
In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schrodinger equations in higher spatial dimensions ($ngeq 2$) and some global well-posedness results with small initial data in critical Besov spaces $B^ s_{2,1}$ are obtained. As by-products, the scattering results with small initial data are also obtained.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا