Helmholtz solitons in power - law optical materials

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures broad beam evolution at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses and liquid crystals. Novel exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three new general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz powerlaw solitons. A new propagation feature, associated with spatial solitons in powerlaw media, constituting a new class of oscillatory solution, is identified.