1,052 research outputs found
Conserved energies for the one dimensional Gross-Pitaevskii equation
We prove the global-in-time well-posedness of the one dimensional
Gross-Pitaevskii equation in the energy space, which is a complete metric space
equipped with a newly introduced metric and with the energy norm describing the
regularities of the solutions. We establish a family of conserved
energies for the one dimensional Gross-Pitaevskii equation, such that the
energy norms of the solutions are conserved globally in time. This family of
energies is also conserved by the complex modified Korteweg-de Vries flow
A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces
We consider the cubic Nonlinear Schrodinger Equation in one space dimension,
either focusing or defocusing. We prove that the solutions satisfy a-priori
local in time H^s bounds in terms of the H^s size of the initial data for s
greater than or equal to -1/6.Comment: 27 pages very minor misprints corrected (see formulas (4), (7)
- …