Nonlinear Dynamics
Nonlinear wave equations, ubiquitous in physics, were pioneered by discoveries of chaotic behavior in simple systems by Fermi, Pasta, Ulam, and Tsingou and by Feigenbaum.

In non-linear dynamics, a system can tend to evolve to a set of states, whatever its starting conditions. Image from wikimedia commons: https://commons.wikimedia.org/wiki/File:Poisson_saturne_revisited.jpg
Summary
Nonlinear wave equations are ubiquitous throughout physics, including the sine-Gordon equation (e.g., nonlinear pendulum, superconducting Josephson junctions), the nonlinear Schrodinger equation (e.g., light propagation in waveguides, Bose-Einstein condensates in a trap, Langmuir waves in hot plasmas) and the Korteweg-de Vries equation (shallow water waves, internal waves). Two watershed events at LANL laid their foundation.
In a groundbreaking computer simulation (1953), Fermi, Pasta, Ulam, and Tsingou discovered that a string comprising non-linear springs shows an unusual behavior, wandering from one pattern of motion to another, and from time to time piling all its energy into a single mode. Two decades later, Feigenbaum, with only a hand calculator, discovered a new universal constant in the behavior of non-linear systems. These discoveries opened applications in control systems, Earth systems such as ocean currents, aerodynamics, chaotic systems, economics, and more. For example, solitons occur both in optical fibers and as self-trapped excitations on biological molecules.
Contributing author
Avadh Saxena
References
The first simulation with nonlinear springs and its consequences are highlighted in:
- Fermi, Pasta, Ulam, and a mysterious lady, Dauxois, Thierry, Physics Today 61 (2008): 55.
The recursive relations exhibiting infinite bifurcation and universality were reported in:
- Quantitative universality for a class of nonlinear transformations, Feigenbaum, Mitchell, Journal of Statistical Physics 19 (1978): 25.