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The '''small amplitude limit''' for a nonlinear equation arises when considering initial position <math>u(0)</math> of the form <math>u(0) = \epsilon f</math> for some fixed <math>f</math> and a small parameter <math>\epsilon > 0</math>, in the limit <math>\epsilon \to 0</math>. For equations which are second-order in time, such as [[wave equations|nonlinear wave equations]], one must also specify an initial velocity <math>u_t(0) = \epsilon g</math>. For bounded times, the small amplitude limit is usually just the linear counterpart of the equation; however when analyzing long times (e.g. times comparable to <math>1/\epsilon</math>), significant nonlinear effects may still occur in the limit. [[Category:limits]]

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