The Einstein field equations are nonlinear and very difficult to solve.

Nonlinear optics (NLO) is the branch of optics that describes the behavior of light in nonlinear media , that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light.

In mathematics, the Benjamin Ono equation is a nonlinear partial integro differential equation thatdescribes one dimensional internal waves in deep water.

Now, if we have evidence, which we now have, that wetlands, forests, unclear monsoon system, the rainforests, behave in this nonlinear way.

And could we even, thanks to major advancements in Earth systems science, identify the thresholds, the points where we may expect nonlinear change?

A field theory showing this property is usually called completely exceptional and Born Infeld theory is the only completely exceptional regular nonlinear electrodynamics.

For example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables.

Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it.

Now, that's also wrong, because traffic happens to be a nonlinear phenomenon, meaning that once you reach above a certain capacity threshold then congestion starts to increase really, really rapidly.

Over longer distances, a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy.

Dynamic systems theory stresses nonlinear connections (e.g., between earlier and later social assertiveness) and the capacity of a system to reorganize as a phase shift that is stage like in nature.

Partial Differential Equations in Cleve Moler Numerical Computing with MATLAB Example problems with solutions at exampleproblems.com Partial Differential Equations at mathworld.wolfram.com Partial Differential Equations at nag.com Dispersive PDE Wiki NEQwiki, the nonlinear equations encyclopedia

The first commercial products involving two dimensionally periodic photonic crystals are already available in the form of photonic crystal fibers, which use a microscale structure to confine light with radically different characteristics compared to conventional optical fiber for applications in nonlinear devices and guiding exotic wavelengths.