Results 71 to 80 of about 3,496 (115)
Nonuniqueness of weak solutions of the nonlinear Schroedinger equation [PDF]
arXiv, 2005 Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schr\"odinger equation, with certain nonlinearities, are not unique. For any $s<0$ there exist nonzero generalized solutions varying continuously in the Sobolev space $H^s$, with identically vanishing initial data.
arxiv
Spectral Theory and Nonlinear PDE: a Survey [PDF]
arXiv, 2005 This is a slightly modified version of the survey article. Minor changes to the text and the references have been made.
arxiv
Strichartz estimates for the magnetic Schrödinger equation [PDF]
arXiv, 2005 We prove global, scale invariant Strichartz estimates for the linear magnetic Schr\"odinger equation with small time dependent magnetic field. This is done by constructing an appropriate parametrix. As an application, we show a global regularity type result for Schr\"odinger maps in dimensions $n\geq 6$.
arxiv
Rough solutions of a Schroedinger - Benjamin - Ono system [PDF]
arXiv, 2005 The Cauchy problem for a coupled Schroedinger and Benjamin - Ono system is shown to be globally well-posed for a class of data without finite energy. The proof uses the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.
arxiv
Single--peaks for a magnetic Schrödinger equation with critic al growth [PDF]
arXiv, 2006 We prove existence results of complex-valued solutions for a semilinear Schr\"odinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory.
arxiv
Advanced Nonlinear Studies, 2019 We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in ℝN{\mathbb{R}^{N}} (N≥2{N\geq 2}):
Hirata Jun, Tanaka Kazunaga
doaj +1 more source
On generating functions in additive number theory, II: lower-order terms and applications to PDEs. [PDF]
Math Ann, 2021 Brandes J +4 more
europepmc +1 more source
Small noise asymptotic of the timing jitter in soliton transmission [PDF]
arXiv, 2006 This submission has been withdrawn because it is a duplicate of [math.PR/0609434].
arxiv
Singularly Perturbed Fractional Schrödinger Equation Involving a General Critical Nonlinearity
Advanced Nonlinear Studies, 2018 In this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schrödinger problem:
Jin Hua, Liu Wenbin, Zhang Jianjun
doaj +1 more source
On Strichartz estimates for Schrödinger operators in compact manifolds with boundary [PDF]
arXiv, 2006 We prove local Strichartz estimates on compact manifolds with boundary. Our results also apply more generally to compact manifolds with Lipschitz metrics.
arxiv