We explore the exact optical similaritons of a generalized nonlinear Schrodinger equation(GNLSE) with space-time modulated
dispersion, nonlinearity, external potential and inhomogeneous source. As an application, we study the dynamics of
these similaritons for a spatial Bessel modulated nonlinearity.
We demonstrate that the localized nonlinear gain induces stable chirped dissipative double-kink, fractional-transform,
bell, and kink type solitons in optical mediawith quadratic nonlinearity. To compensate spatially uniform loss in both
fundamental-frequency (FF) and second-harmonic (SH) component of the system, a strongly localized hot-spot, carrying
the nonlinear gain, is added, acting either on FF component or on the SH one.