Analysis

2001/03/21 by Elliott H. Lieb, Michael Loss · 6 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Quantum chaos and dynamical systems #Computer science

paper · pdf · doi:10.1090/gsm/014

openalex publication_date 2001/03/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

The defocusing Davey-Stewartson II equation has been shown in numerical experiments to exhibit behavior in the semiclassical limit that qualitatively resembles that of its one-dimensional reduction, the defocusing nonlinear Schrdinger equation, namely the generation from smooth initial data of regular rapid oscillations occupying domains of space-time that become well-defined in the limit.

Citations

• Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

Cited by

• A Simple Proof of Hardy-Lieb-Thirring Inequalities
• A Stochastic‐Variational Model for Soft Mumford‐Shah Segmentation
• Exponential convergence to equilibrium in a coupled gradient flow system modeling chemotaxis
• Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature
• The Brunn-Minkowski inequality
• Shing-Tung Yau [wikipedia]