Construction of nonlinear quasimodes near elliptic periodic orbits
作者： Pierre Albin , Hans Christianson , Jeremy L. Marzuola , Laurent Thomann
DOI: 10.1016/J.PHYSD.2011.10.011
关键词: Mathematical physics 、 Geometry 、 Mathematics 、 Periodic orbits 、 Nonlinear system 、 Nonlinear Schrödinger equation 、 Geodesic
摘要: Abstract We generalize to arbitrary manifolds with elliptic periodic geodesics a quasimode construction for the nonlinear Schrodinger equation first discovered by last author.
harvard.edu
elsevier.com
sci-hub.se 参考文章(18)
Fernando Cardoso, Georgi Popov, None, Quasimodes with exponentially small errors associated with elliptic periodic rays Asymptotic Analysis. ,vol. 30, pp. 217- 247 ,(2002)
Lars Hörmander, The analysis of linear partial differential operators Springer-Verlag. ,(1990)
Jerrold E. Marsden, Alan Weinstein, Review: Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, and Nolan R. Wallach, Symplectic geometry and Fourier analysis Bulletin of the American Mathematical Society. ,vol. 1, pp. 545- 553 ,(1979) , 10.1090/S0273-0979-1979-14617-2
Hans Christianson, Jeremy L Marzuola, Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space Nonlinearity. ,vol. 23, pp. 89- 106 ,(2010) , 10.1088/0951-7715/23/1/005
Rafe Mazzeo, Frank Pacard, Foliations by constant mean curvature tubes Communications in Analysis and Geometry. ,vol. 13, pp. 633- 670 ,(2005) , 10.4310/CAG.2005.V13.N4.A1
Hans Christianson, Semiclassical non-concentration near hyperbolic orbits Journal of Functional Analysis. ,vol. 246, pp. 145- 195 ,(2007) , 10.1016/J.JFA.2006.09.012
Victor Guillemin, Alan Weinstein, Eigenvalues associated with a closed geodesic Bulletin of the American Mathematical Society. ,vol. 82, pp. 92- 95 ,(1976) , 10.1090/S0002-9904-1976-13972-9
Hans Christianson, Quantum Monodromy and nonconcentration near a closed semi-hyperbolic orbit Transactions of the American Mathematical Society. ,vol. 363, pp. 3373- 3438 ,(2011) , 10.1090/S0002-9947-2011-05321-3
Nicolas Burq, P Gerard, N Tzvetkov, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds American Journal of Mathematics. ,vol. 126, pp. 569- 605 ,(2004) , 10.1353/AJM.2004.0016
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge, On Strichartz estimates for Schrödinger operators in compact manifolds with boundary Proceedings of the American Mathematical Society. ,vol. 136, pp. 247- 256 ,(2008) , 10.1090/S0002-9939-07-09114-9