Nonlinear wave equations: Constraints on periods and exponential bounds for periodic solutions

DOI10.1215/S0012-7094-97-08805-0zbMath0885.35078OpenAlexW1572237783MaRDI QIDQ1363174

Randall Pyke, Israel Michael Sigal

Publication date: 23 April 1998

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-97-08805-0

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Spectral theory and eigenvalue problems for partial differential equations (35P99) Second-order nonlinear hyperbolic equations (35L70) Schrödinger operator, Schrödinger equation (35J10)

Cites Work

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• Periodic soliton solutions to nonlinear Klein-Gordon equations on \({\mathbb{R}}^ 2\)
• \(L^2\)-exponential lower bounds to solutions of the Schrödinger equation
• Periodic nonlinear waves on a half-line
• Minimal periods for solutions of semilinear wave equations in exterior domains and for solutions of the equations of nonlinear elasticity
• Absence of singular continuous spectrum for certain self-adjoint operators
• Complex-valued time-periodic solutions and breathers of nonlinear wave equations
• Existence of solitary waves in higher dimensions
• Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
• On the existence and structure of stationary states for a nonlinear Klein-Gordon equation
• Decay properties of periodic, radially symmetric solutions of Sine‐Gordon‐type equations
• The Functional Calculus

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