Rogue waves on the double-periodic background in the focusing nonlinear Schrödinger equation

The double-periodic solutions of the focusing nonlinear Schrödinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues. Furthermore, we characterize the Lax spectrum for the double-periodic solutions and analyze rogue waves arising on the background of such solutions. Magnification of the rogue waves is studied numerically.