The Modulated Phase Shift for Strongly Nonlinear, Slowly Varying, and Weakly Damped Oscillators

DOI10.1137/0148042zbMath0667.34048OpenAlexW1993974887MaRDI QIDQ3819363

Richard Haberman, F. Jay Bourland

Publication date: 1988

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0148042

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05) Dynamical systems and ergodic theory (37-XX)

Related Items (10)

The capture of a particle into resonance at potential hole with dissipative perturbation ⋮ Connection across a Separatrix with Dissipation ⋮ The slowly varying phase shift for perturbed, single and multi-phased, strongly nonlinear, dispersive waves ⋮ Remark on the phase shift in the Kuzmak-Whitham ansatz ⋮ On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation ⋮ Hard Loss of Stability in Painlevé-2 Equation ⋮ Scattering of trajectories at a separatrix under autoresonance ⋮ Autoresonance in a dynamic system ⋮ Phase Shift Modulations for Stable, Oscillatory, Traveling, Strongly Nonlinear Waves ⋮ Autoresonance in a model of a terahertz wave generator

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