Rogue waves solutions on the elliptic background of an extended (3 + 1)‐dimensional nonlinear Schrödinger equation

We construct rogue wave solutions of an extended (3 + 1)‐dimensional nonlinear Schrödinger equation on the Jacobian elliptic function background. The modulational stability of the plane wave background is analyzed. We derive the periodic wave solutions and non‐periodic wave solutions of the Lax spectral problem. Making use of the non‐periodic solutions, we construct rogue waves on the cnoidal background via one‐ and two‐fold Darboux transformation. By using one‐fold Darboux transformation, rogue waves on the dnoidal background are also proposed.