Perturbation method for periodic solutions of nonlinear jerk equations

DOI10.1016/j.physleta.2008.03.027zbMath1221.70017OpenAlexW2021282919MaRDI QIDQ719130

D. Kharzeev

Publication date: 27 September 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2008.03.027

zbMATH Keywords

Newton's methodLindstedt-Poincaré methodbookkeeping parameternonlinear jerk equation

Mathematics Subject Classification ID

General perturbation schemes for nonlinear problems in mechanics (70K60) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) (n)-body problems (70F10) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Related Items (11)

Global residue harmonic balance method to periodic solutions of a class of strongly nonlinear oscillators ⋮ Iteration calculations of periodic solutions to nonlinear jerk equations ⋮ Effective approximate methods for strongly nonlinear differential equations with oscillations ⋮ Comparison of two iteration procedures for a class of nonlinear jerk equations ⋮ Existence of positive periodic solution for variable-coefficient third-order differential equation with singularity ⋮ The simplest approach to solving the cubic nonlinear jerk oscillator with the non‐perturbative method ⋮ Approximate periodic solutions for oscillatory phenomena modelled by nonlinear differential equations ⋮ Approximate methods based on order reduction for the periodic solutions of nonlinear third-order ordinary differential equations ⋮ Vibration control by nonlocal feedback and jerk dynamics ⋮ Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations ⋮ A Volterra integral formulation for determining the periodic solutions of some autonomous, nonlinear, third-order ordinary differential equations

Cites Work

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• An analytical approximate technique for a class of strongly non-linear oscillators
• A classical perturbation technique which is valid for large parameters
• Harmonic balance approach to periodic solutions of non-linear jerk equations
• A classical perturbation technique that works even when the linear part of restoring force is zero
• Comparison of two Lindstedt–Poincaré-type perturbation methods
• A Perturbation Technique that Works Even When the Non-Linearity is Not Small
• Generalization of the Senator–Bapat Method to Systems having Limit Cycles

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