General rogue waves in the focusing and defocusing Ablowitz-Ladik equations

Abstract

General rogue waves in the focusing and defocusing Ablowitz-Ladik equations are derived by the bilinear method. In the focusing case, it is shown that rogue waves are always bounded. In addition, fundamental rogue waves reach peak amplitudes which are at least three times that of the constant background, and higher-order rogue waves can exhibit patterns such as triads and circular arrays with different individual peaks. In the defocusing case, it is shown that rogue waves also exist. In addition, these waves can blow up to infinity in finite time.

24 pages, 6 figures

References in corpus (3)

• High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
• Akhmediev breathers, Ma solitons and general breathers from rogue waves: A case study in Manakov system
• The Rogue Waves with Quintic Nonlinearity and Nonlinear Dispersion effects in Nonlinear Optical Fibers

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• General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system
• General rogue waves in the Boussinesq equation
• Rogue Waves in (2+1)-Dimensional Three-Wave Resonant Interactions
• General rogue wave solutions to the discrete nonlinear Schrödinger equation
• Discrete Rogue waves in an array of waveguides
• Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schrödinger equations
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Solitary waves in the Ablowitz-Ladik equation with power-law nonlinearity
• Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons
• A focusing and defocusing semi-discrete complex short pulse equation and its varioius soliton solutions
• On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equation
• General rogue waves in the three-wave resonant interaction systems