J. Chen, D.E. Pelinovsky, and R.E. White

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

Physical Review E 100, 052219 (18 pages) (2019)

Abstract:
The double-periodic solutions of the focusing nonlinear Schrodinger 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 their background. Magnification of the rogue waves is studied numerically.

Keywords:
nonlinear Schrodinger equation, double-periodic solutions, rogue waves, Lax spectrum.