Invariants for time-dependent potentials: Use of self-similar techniques

DOI10.1016/0167-2789(87)90122-9zbMath0656.70014OpenAlexW2025612892MaRDI QIDQ1110356

S. Bouquet, Marc R. Feix, H. Ralph Lewis

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90122-9

zbMATH Keywords

self-similar solutionsone-dimensional motiontime-dependent nonlinear Hamiltonian systems

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view, Representations of one-dimensional Hamiltonians in terms of their invariants, Hamiltonian structure and integrability of the stationary Kuramoto–Sivashinsky equation, Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation, Extension of Giacomini’s results concerning invariants for one-dimensional time-dependent potentials, First integrals and symmetries of time-dependent Hamiltonian systems

Cites Work

• First integrals for one-dimensional particle motion in a non-linear, time-dependent potential field
• A direct construction of first integrals for certain non-linear dynamical systems
• Similarity methods for differential equations
• Nonlinear time-dependent anharmonic oscillator: Asymptotic behavior and connected invariants
• Invariants for dissipative nonlinear systems by using rescaling
• A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians
• Exact time-dependent solutions of the Vlasov–Poisson equations
• Exact, time-dependent solutions of the one-dimensional Vlasov–Maxwell equations