Exact solitary- and periodic-wave modes in coupled equations with saturable nonlinearity

We demonstrate that the known method, based on the Hirota bilinear operator, generates classes of exact solutions to a system of coupled nonlinear Schrödinger (CNLS) equations with nonpolynomial nonlinearity, either rational or algebraic (the latter involves a square root). The choice of the CNLS equations is suggested by known models for photorefractive media and Bose–Einstein condensation. The solutions are, generally, periodic, and they form families expressed in terms of the Jacobi elliptic functions, the elliptic modulus k   being a free parameter of the family. In the limit case corresponding to the infinite period (k=1k=1), the solutions amount to solitons. In some cases, the exact solutions may feature patterns with two peaks per period. Exact solutions are also found in a single NLS equation with a rational saturable nonlinearity and periodic potential in the form of squared Jacobi sine.