Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Not in a straight line.
 adj. Mathematics Occurring as a result of an operation that is not linear.
 adj. Mathematics Containing a variable with an exponent other than one. Used of an equation.
 adj. Of or relating to a system of equations whose effects are not proportional to their causes. Such a set of equations can be chaotic.
 adj. Of or relating to a device whose behavior is described by a set of nonlinear equations and whose output is not proportional to its input.
 adj. Of or relating to the output of such a device.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. not lying on a straight line
 adj. whose atoms do not lie in a straight line
 adj. having a product of independent variables, or a variable with an exponent not equal to one
 adj. whose output is not directly proportional to its input
 adj. erratic and unpredictable; tending to jump back and forth
from the GNU version of the Collaborative International Dictionary of English
 adj. Not depictable graphically as a straight line; not changing by a constant amount for each unit of time, distance, or other independent variable. Opposite of
linear .  adj. Containing variables of greater than the first degree;  of an equation. Opposite of
linear .  adj. Represented by equations containing variables of greater than the first degree;  of physical processes or relationships. Opposite of
linear .
from The Century Dictionary and Cyclopedia
 Not linear; in mathematics, not of the first degree.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. designating or involving an equation whose terms are not of the first degree
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

I am quite familiar with the standard scientific application of ˜irreducible complexity 'in nonlinear science.

I am quite familiar with the standard scientific application of 'irreducible complexity' in nonlinear science.

My research in nonlinear optics continued with special emphasis on interactions of picosecond and femtosecond laser pulses with condensed matter and of collisioninduced optical coherences.

Digitalpower mavens also brag about "nonlinear"  control approaches, but these loops prevent you from connecting a network analyzer on digitalpower chips.

A further analysis, where G. Nicolis played a key role, showed that an unexpected phenomenon appeared while one considered the fluctuation problem in nonlinear systems far from equilibrium: the distribution law of fluctuations depends on their scale, and only "small fluctuations" follow the law proposed by Einstein. 29 After a prudent reception, this result is now widely accepted, and the theory of nonequilibrium fluctuations is fully developing now, so as to allow us to expect important results in the following years.

The U.S. tax code is highly complex (what mathematicians would call nonlinear and discontinuous) and small differences in your circumstances can make a big difference in determining whether converting is for you.

There have been hundreds of manpower hours and computer resources spent on the so called nonlinear normal mode initialization NNMI procedure.

So the company uses a socalled nonlinear, or "frequency doubling," crystal.

I mean, now I can write things and write the software so that it's completely nonlinear, which is really fun for me.

One simple model for this is a wave equation known as the nonlinear Schrödinger equation (NLS), in which a normal and perfectly accountable (by the standard linear model) wave begins to 'soak' energy from the waves immediately fore and aft, reducing them to minor ripples compared to other waves.
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