The Cauchy problem of the nonlinear Schrödinger equations in \(\mathbb R^{1+1}\)

DOI10.1007/s10255-007-0398zbMath1137.35432OpenAlexW2127888495MaRDI QIDQ2480088

Gui Xiang Xu

Publication date: 31 March 2008

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-007-0398

zbMATH Keywords

Besov spaceCauchy problemself-similar solutionSchrödinger equationLittlewood-Paley decomposition

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10)

Cites Work

• On the asymptotic behavior of large radial data for a focusing nonlinear Schrödinger equation
• Dispersive estimates and the 2D cubic NLS equation.
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations
• Nonlinear Schrödinger equations in the Sobolev space of critical order
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Well-posedness results for the generalized Benjamin-Ono equation with small initial data.
• On existence and scattering with minimal regularity for semilinear wave equations
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• On the Cauchy Problem for the Generalized Korteweg-de Vries Equation
• ON THE CAUCHY PROBLEM IN BESOV SPACES FOR A NON-LINEAR SCHRÖDINGER EQUATION
• Global strichartz estimates for nonthapping perturbations of the laplacian
• Self-similar solutions for navier-stokes equations in
• Scattering Theory and Self-Similar Solutions for the Nonlinear Schrödinger Equation
• Self-similar solutions for nonlinear Schrödinger equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Cauchy problem of the nonlinear Schrödinger equations in \(\mathbb R^{1+1}\)