Analyticity of the scattering operator for semilinear dispersive equations
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Publication:842424
DOI10.1007/s00220-008-0599-xzbMath1173.35677arXiv0801.3774OpenAlexW2162926610MaRDI QIDQ842424
Rémi Carles, Isabelle Gallagher
Publication date: 25 September 2009
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0801.3774
KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Second-order nonlinear hyperbolic equations (35L70) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse scattering problems in quantum theory (81U40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)
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Cites Work
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- Scattering theory in the energy space for a class of nonlinear Schrödinger equations
- Scattering and complete integrability in the massive \(\phi ^ 4\) theory
- Semilinear Schrödinger flows on hyperbolic spaces: scattering in \(H^{1}\)
- The inverse scattering problem for Schrödinger and Klein-Gordon equations with a nonlocal nonlinearity
- Scattering theory in the energy space for a class of nonlinear wave equations
- On the wave operator for the critical nonlinear Schrödinger equation
- Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space
- The cubic nonlinear Schrödinger equation in two dimensions with radial data
- Nonlinear scattering theory at low energy
- Analyticity of the scattering operator for the nonlinear Klein-Gordon equation with cubic nonlinearity
- Rapidly decaying solutions of the nonlinear Schrödinger equation
- Abstract non linear wave equations
- On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
- Regularity results for nonlinear wave equations
- Birkhoff normal form for some nonlinear PDEs
- Scattering theory: some old and new problems
- Energy scattering for Hartree equations
- Remarks on scattering for nonlinear Schrödinger equations
- Oscillations of concentration effects in semilinear dispersive wave equations
- Analyticity of scattering for the \(\phi ^ 4\) theory
- Conformal conservation law, time decay and scattering for nonlinear wave equations
- Global and unique weak solutions of nonlinear wave equations
- Generalized Strichartz inequalities for the wave equation
- 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 global Goursat problem and scattering for nonlinear wave equations
- Remarques sur les mesures de Wigner
- Scattering and complete integrability in conformally invariant nonlinear theories
- Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
- Endpoint Strichartz estimates
- High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations
- The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
- Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds
- Integrals of nonlinear equations of evolution and solitary waves
- On a nonlinear scattering operator
- Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations
