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

DOI10.1088/0951-7715/23/1/005zbMath1184.35291arXiv0905.1848OpenAlexW1982532330MaRDI QIDQ5851951

Hans Christianson, Jeremy L. Marzuola

Publication date: 26 January 2010

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.1848

zbMATH Keywords

stabilitynonlinear Schrödinger equationhyperbolic space

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items (14)

Extremal values of the (fractional) Weinstein functional on the hyperbolic space ⋮ A special class of nonlinear hypoelliptic equations on spheres ⋮ Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space ⋮ Construction of nonlinear quasimodes near elliptic periodic orbits ⋮ Uniqueness of the ground state of the NLS on \(\mathbb{H}^d\) via analytical and topological methods ⋮ Uniqueness of radial solutions of semilinear elliptic equations on hyperbolic space ⋮ Existence and Asymptotics of Nonlinear Helmholtz Eigenfunctions ⋮ Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space ⋮ Nonlinear Bound States on Weakly Homogeneous Spaces ⋮ Higher dimensional vortex standing waves for nonlinear Schrödinger equations ⋮ Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models ⋮ Qualitative properties of stationary solutions of the NLS on the hyperbolic space without and with external potentials ⋮ Existence and Stability of Schrödinger Solitons on Noncompact Manifolds ⋮ Dispersive estimates for scalar and matrix Schrödinger operators on \(\mathbb H^{n+1}\)

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