Focusing

From DispersiveWiki


Informally, an equation is focusing (or attractive) if the nonlinearity tends to act to reinforce the solution when it is large and diminish it when it is small, thus counteracting the effects of dispersion. The opposite of focusing is defocusing, though there do exist nonlinear equations which are neither focusing nor defocusing as the nonlinearity exhibits no bias towards helping or hindering the dispersion.

Focusing equations tend to have an indefinite Hamiltonian and are more likely to blow up than defocusing ones. They are also likely to support soliton solutions.