A Hamilton–Jacobi approach to the control of the trapping time of a soliton by an external potential

DOI10.1090/S0033-569X-05-00950-0zbMath1089.35069OpenAlexW2088921347MaRDI QIDQ5700384

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Publication date: 28 October 2005

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0033-569x-05-00950-0

zbMATH Keywords

Hamilton-Jacobi equationviscosity solutionnonlinear Schrödinger equationsoliton control

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Cites Work

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• Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations
• Conditions for soliton trapping in random potentials using Lyapunov exponents of stochastic ODEs
• Soliton perturbations and the random Kepler problem
• An Approximation Scheme for the Minimum Time Function
• Two Approximations of Solutions of Hamilton-Jacobi Equations
• A Viscosity Solutions Approach to Shape-From-Shading
• User’s guide to viscosity solutions of second order partial differential equations
• Asymptotic Transmission of Solitons through Random Media
• A fast sweeping method for Eikonal equations
• Motion of 2D Schrödinger Solitary Waves in the Presence of Random External Potentials
• A Boundary Value Problem for the Minimum-Time Function
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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