Optical rogue waves associated with the negative coherent coupling in an isotropic medium

Abstract

Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported. We construct and discuss a family of the vector rogue-wave solutions, including the bright rogue waves, four-petaled rogue waves, and dark rogue waves. A bright rogue wave without a valley can split up, giving birth to two bright rogue waves, and an eye-shaped rogue wave can split up, giving birth to two dark rogue waves.

Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

“…Then, we get the eigenfunction (ϕ 1 [3], ϕ 2 [3]) T , which is a solution for Lax pair (4) at [2] ψ ψ = and λ = λ 1 , whereas ϕ 1 [3] and ϕ 2 [3] are the functions of x and t. Meanwhile, we can derive the third-order solutions for (2) as…”

“…Rogue waves, also known as the freak waves or monster waves, have been used to describe the isolated and large waves with higher amplitudes than the average wave crests around in the ocean and have also been seen in the Bose-Einstein condensates, plasmas, and optical fibres [1][2][3][4][5][6]. A model for the rogue waves in optical fibre communication is the 'self-focusing' nonlinear Schrödinger (NLS) equation [7,8], 2 1 | | 0, 2…”

On a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli Equation

“…where Θ is a function of x, y, z, and t. (2). By the way, Lax pairs (38) can also be obtained via the Bell polynomials.…”

“…In the fluid and plasma dynamics, special cases of (2) are seen as follows: (a) When y = z, u(x, y, t) = (η, t) =  [x + χ(y), t] with as χ an analytic function of y, (2) degenerates into the KdV equation [37],…”

“…Among the nonlinear evolution equations (NLEEs) [1][2][3][4][5], Korteweg-de Vries (KdV)-type equations can be used to describe the shallow water waves of long wavelength and small amplitude, stratified internal waves and ionacoustic waves in plasmas [6,7]. As a (2+1)-dimensional KdV-type equation, the Boiti-Leon-Manna-Pempinelli (BLMP) equation can be considered as a model for the incompressible fluid [7][8][9], which is…”