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

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.

24 pages, 8 figures, 3 tables

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Cited by in corpus (13)

• Multi-breathers and high order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• Soliton gas in integrable dispersive hydrodynamics
• Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
• Doubly periodic solutions of the focusing nonlinear Schrödinger equation: recurrence, period doubling and amplification outside the conventional modulation instability band
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• Stability of elliptic function solutions for the focusing modified KdV equation
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• Rogue waves in extended Gross-Pitaevskii Models with a Lee-Huang-Yang correction
• Rogue waves on the periodic wave background in the focusing nonlinear Schrodinger equation
• Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves