Modified scattering for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions
DOI10.1063/5.0052299zbMath1469.81076OpenAlexW3177918734MaRDI QIDQ5009713
Nakao Hayashi, Pavel I. Naumkin
Publication date: 5 August 2021
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/5.0052299
Asymptotic behavior of solutions to PDEs (35B40) Pseudodifferential operators as generalizations of partial differential operators (35S05) Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Functional calculus for linear operators (47A60) NLS equations (nonlinear Schrödinger equations) (35Q55) (2)-body potential quantum scattering theory (81U05) Initial value problems for nonlinear higher-order PDEs (35G25)
Cites Work
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- Dispersive blowup of solutions of generalized Korteweg-de Vries equations
- Dispersive blow-up for nonlinear Schrödinger equations revisited
- Third-order dispersion for generating optical rogue \textit{solitons}
- The initial value problem for the cubic nonlinear Klein-Gordon equation
- Sur quelques généralisations de l'équation de Korteweg-de Vries
- Long range scattering for nonlinear Schrödinger equations in one space dimension
- Gain of regularity for equations of KdV type
- On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators
- A higher-order nonlinear Schrödinger equation with variable coefficients.
- Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion
- On the (generalized) Korteweg-de Vries equation
- Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
- Higher-order nonlinear Schrödinger equation in 2D case
- Long range scattering for the nonlinear Schrödinger equation with higher order anisotropic dispersion in two dimensions
- Self-Focusing with Fourth-Order Dispersion
- On the inhomogeneous fourth-order nonlinear Schrödinger equation
- GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION
- The L 2 -Boundedness of Pseudodifferential Operators
- Local Smoothing Properties of Dispersive Equations
- Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
- Analyticity of Solutions of the Korteweg–De Vries Equation
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- THE CAUCHY PROBLEM FOR A THIRD ORDER NONLINEAR SCHRÖDINGER EQUATION
- Critical exponents and collapse of nonlinear Schr dinger equations with anisotropic fourth-order dispersion
- A Class of Bounded Pseudo-Differential Operators