#Nonlinear schrodinger equation series
#Nonlinear schrodinger equation free

Sharp energy criteria and singularity of blow-up solutions for the Davey-Stewartson system, Commun. Sharp threshold for blowup and global existence in nonlinear SchrГ¶dinger equations under a harmonic potential, Comm. Zhang, Cross-constrained variational problem and nonlinear SchrГ¶dinger equation, Foundations of Computational Mathematics, World Scientific Publishing, River Edge, NJ, 2002,457вЂ“469. Stability of attractive Bose-Einstein condensates, J. Xu, Cross-constrained problems for nonlinear SchrГ¶diner equation with harmonic potential, Electron. Nonlinear SchrГ¶dinger equations and sharp interpolation estimates, Comm. Global solutions and stable ground states of nonlinear SchrГ¶dinger equations, Phys.

#Nonlinear schrodinger equation series

International Series of Monographs on Physics, The Clarendon Press, Oxford University Press, Oxford, 2003. Zhang, Mass concentration for nonlinear SchrГ¶dinger equation with partial confinement, J. Saddle points and instability of nonlinear hyperbolic equations, Israel. Strong instability of standing waves for nonlinear SchrГ¶dinger equations with a partial confinement, Commun. Lev, Strongly dipolar Bose-Einstein condensate of dysprosium, Phys. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear SchrГ¶dinger equation in the radial case, Invent. Pomeau, Nonlinear aspects of the theory of Bose-Einstein condensates, Nonlinearity, 14 (2001), R25вЂ“R62. Phys., 283 (2008), 93-125.ДЄ sharp condition for scattering of the radial 3D cubic nonlinear SchrГ¶dinger equation, Comm. Sharp threshold of global existence and insatbility of standing wave for a Davey-Stewartson system, Comm. Scattering for the non-radial 3D cubic nonlinear SchrГ¶dinger equation, Math.

On the Gross-Pitaevskii equation for trapped dipolar quantum gases, Nonlinearity, 21 (2008), 2569-2590. Cazenave, Semilinear SchrГ¶dinger Equations, Courant Institute of Mathematical Sciences, American Mathematical Society, New York, 2003. Visciglia,Д®xistence and stability of standing waves for supercritical NLS with a partial confinement, Commun. Mathematical theory and numerical methods for Bose-Einstein condensation, Kinet.

#Nonlinear schrodinger equation free

Numerical simulations of x-ray free electron lasers (XFEL), Multiscale Model. This has created an enormous amount of new mathematical problems for mathematicians.Scattering for nonlinear SchrГ¶dinger equation under partial harmonic confinement, Comm. The last few years have witnessed a rapid development in research of NLS-related applications such as optical communications, laser surgeries, remote sensing and the BEC. It admits solutions in the form of coherent structures like vortices that define states that can be excited in super helium. NLS also appears in the description of the Bose-Einstein Condensate (BEC), a context where it is often called the Gross-Pitaevskii equation. It arises in various physical contexts in the description of nonlinear waves such as propagation of a laser beam in a medium whose index of reflection is sensitive to the wave amplitude, water waves at the free surface of an ideal and plasma waves.

The nonlinear SchrГ¶dinger (NLS) equation provides a canonical description for the envelope dynamics of a quasi-monochromatic plane wave propagating in a weakly nonlinear dispersive medium when dissipative processes are negligible.