Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space

Hans Christianson, Jeremy L. Marzuola

Type: Article

Publication Date: 2009-12-10

Citations: 31

DOI: https://doi.org/10.1088/0951-7715/23/1/005

Abstract

We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.

Locations

Nonlinearity - View
arXiv (Cornell University) - View - PDF
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+ PDF Chat	Nonlinear scalar field equations	1992	W. Rother
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+ PDF Chat	Instability of nonlinear bound states	1985	Jalal Shatah Walter A. Strauss
+ PDF Chat	Semilinear Schrödinger flows on hyperbolic spaces: scattering in H 1	2009	Alexandru D. Ionescu Gigliola Staffilani
+	Rearrangement Inequalities with Application to Ratios of Heat Kernels	2005	Cristina Draghici
+	Orbital stability of standing waves for some nonlinear Schr�dinger equations	1982	Thierry Cazenave Pierre‐Louis Lions
+	Stability theory of solitary waves in the presence of symmetry, II	1990	Manoussos G. Grillakis Jalal Shatah Walter A. Strauss