The cubic fourth-order Schrödinger equation
By Benoit Pausader. 2008
184 citations recorded by the source corpus.
Fourth-order Schrodinger equations have been introduced by Karpman and Shagalov to take into account the role of small fourth-order dispersion terms in the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. In this paper we investigate the cubic defocusing fourth-order Schrodinger equation i∂tu+Δ2u+|u|2u=0 in arbitrary space dimension Rn for arbitrary initial data. We prove that the equation is globally well-posed when n⩽8 and ill-posed when n⩾9, with the additional important information that scattering holds true when 5⩽n⩽8.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ac8ddb3319d50df52f3da54a809d5523ee11307d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Scattering for the focusing L2-supercritical and Ḣ2-subcritical biharmonic NLS equations (2015, background): “Segata in [27] proved scattering inR1 for the cubic nonlinearity; while in higher dimensions, the scattering results were obtained in [19, 24].”