Doubly periodic wave solution to two-dimensional diffractive-diffusive Ginzburg–Landau equation

An algebraic method is applied to obtain a series of exact solutions to the two-dimensional cubic Ginzburg–Landau equation with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. A Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method, is proposed to obtain the exact periodic solutions. It is shown that the periodic solutions obtained by using Jacobi elliptic function expansion method include some like-kink wave solutions and like-shock wave solutions.