Nonlinear systems

Resonant interaction

In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most nonlinear systems; instabilities offer insight into high-dimensional chaos and turbulence. (Wikipedia).

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If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.

From playlist Listening

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DNA | Normal mode | Pseudopotential | Charged particle | Cross-spectrum | Action-angle coordinates | Soliton | Entropy | S-matrix | Wave vector | Brillouin zone | Nonlinear system | Fermi–Pasta–Ulam–Tsingou problem | Chaos theory | Entropic force | Mixing (mathematics) | Henri Poincaré | Canonical transformation | Number theory | Electron microscope | Turbulence | Valence electron | Three-wave equation | Klein–Gordon equation | Wave | Arnold tongue | Partial differential equation | Amino acid | Canonical coordinates | Matrix (mathematics) | Fourier transform