共查询到10条相似文献,搜索用时 62 毫秒
1.
Jun-ichi Segata 《Proceedings of the American Mathematical Society》2004,132(12):3559-3568
We consider the initial value problem for the fourth order nonlinear Schrödinger type equation (4NLS) related to the theory of vortex filament. In this paper we prove the time local well-posedness for (4NLS) in the Sobolev space, which is an improvement of our previous paper.
2.
Ill-posedness is established for the initial value problem (IVP) associated to the derivative nonlinear Schrödinger equation for data in , . This result implies that best result concerning local well-posedness for the IVP is in . It is also shown that the (IVP) associated to the generalized Benjamin-Ono equation for data below the scaling is in fact ill-posed.
3.
Alexander Kiselev 《Journal of the American Mathematical Society》2005,18(3):571-603
We construct examples of potentials satisfying where the function is growing arbitrarily slowly, such that the corresponding Schrödinger operator has an imbedded singular continuous spectrum. This solves one of the fifteen ``twenty-first century" problems for Schrödinger operators posed by Barry Simon. The construction also provides the first example of a Schrödinger operator for which Möller wave operators exist but are not asymptotically complete due to the presence of a singular continuous spectrum. We also prove that if the singular continuous spectrum is empty. Therefore our result is sharp.
4.
Atanas Stefanov 《Proceedings of the American Mathematical Society》2001,129(5):1395-1401
We prove an endpoint Strichartz estimate for radial solutions of the two-dimensional Schrödinger equation:
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6.
Giorgio Metafune Diego Pallara 《Proceedings of the American Mathematical Society》2002,130(6):1779-1786
We give estimates on the bottom of the essential spectrum of Schrödinger operators in .
7.
Alexander Pankov 《Proceedings of the American Mathematical Society》2008,136(7):2565-2570
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schrödinger equations. Under certain natural assumptions we show that any such solution is continuous and vanishes at infinity. This allows us to interpret the solution as a finite multiplicity eigenfunction of a certain linear Schrödinger operator and, hence, apply well-known results on the decay of eigenfunctions.
8.
David Damanik Dirk Hundertmark 《Proceedings of the American Mathematical Society》2004,132(7):1957-1962
We prove a criterion for absence of decaying solutions for one-dimensional Schrödinger operators. As necessary input, we require infinitely many centers of local reflection symmetry and upper and lower bounds for the traces of the associated transfer matrices.
9.
Franç ois Germinet Abel Klein 《Proceedings of the American Mathematical Society》2003,131(3):911-920
We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.
10.
Daniella Bekiranov Takayoshi Ogawa Gustavo Ponce 《Proceedings of the American Mathematical Society》1997,125(10):2907-2919
An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation,
is locally well-posed for weak initial data . We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.