Weakly nonlinear expansion
= Weakly nonlinear expansion
A weakly nonlinear expansion writes a small disturbance as powers of an amplitude parameter while resolving its evolution on a <slow time>. Near a critical <eigenvalue>, linear detuning and nonlinear interactions enter the same perturbation order. The <Fredholm solvability condition for a self-adjoint operator>, or its adjoint form for a general operator, yields an <amplitude equation> without requiring the full higher-order correction.