Rogue Waves in Higher Order Nonlinear Schrödinger Models

The Lagrange form of the nonlinear Schrödinger equation for low vorticity waves in deep water: rogue wave aspect by

Advantages and limitations of the nonlinear Schrödinger equation in describing the evolution of nonlinear water-wave groups

The nonlinear Schrödinger (NLS) equation is a popular and relatively simple model used extensively to describe the evolution of nonlinear water-wave groups. It is often applied in relation to the appearance of extremely steep (freak, or rogue) waves in the ocean. The limits of the applicability of the NLS equation, and in particular the relevance of the model to rogue waves, are examined here o...

Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation.

In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical i...

Dynamics of Rogue Waves on a Multisoliton Background in a Vector Nonlinear Schrödinger Equation

General higher order rogue waves of a vector nonlinear Schrödinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free parameters are expressed in separation of variables form. These solutions exhibit rogue waves on a multisoliton background. They demonstrate that the structur...

Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential

In this work, based on the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlocal nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects doe...