Solitons supported by localized parametric gain.

We address the existence and properties of one-dimensional solitons maintained by localized parametric gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We found that the family of fundamental solitons is partly stable in focusing nonlinear medium, and completely stable in defocusing medium, while all higher-order solitons are unstable. In addition to numerical results, the existence threshold for the solitons and a particular stable exact solution are obtained in an exact analytical form.