Search results for "Rogue waves"
showing 5 items of 35 documents
Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers
2008
International audience; We report experimental observation and characterization of rogue wave-like extreme value statistics arising from pump-signal noise transfer in a fiber Raman amplifier. Specifically, by exploiting Raman amplification with an incoherent pump, the amplified signal is shown to develop a series of temporal intensity spikes whose peak power follows a power-law probability distribution. The results are interpreted using a numerical model of the Raman gain process using coupled nonlinear Schrödinger equations, and the numerical model predicts results in good agreement with experiment.
Complex rogue wave in the fiber optics
2016
This manuscript presents the generation of complex rogue waves related to nonlinear instabilities occurring through the propagation of light in standard optical fibers. Linear and nonlinear physical phenomena involved are first listed, in particular some of them by analogy with the field of hydrodynamics. The different forms of rogue waves induced by the modulation instability process are then presented. They are also known as "breathers", and they are obtained by solving the nonlinear Schrödinger equation. From these exact solutions, various experimental systems were designed by means of numerical simulations based on two rogue-wave excitation methods. The first one is an exact generation …
8-parameter solutions of fifth order to the Johnson equation
2019
We give different representations of the solutions of the Johnson equation with parameters. First, an expression in terms of Fredholm determinants is given; we give also a representation of the solutions written as a quotient of wronskians of order 2N. These solutions of order N depend on 2N − 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polyno-mials of degree 2N (N +1) in x, t and 4N (N +1) in y depending on 2N −2 parameters. Here, we explicitly construct the expressions of the rational solutions of order 5 depending on 8 real parameters and we study the patterns of their modulus in the plane (x, y) and their …
From first to fourth order rational solutions to the Boussinesq equation
2020
Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N , the numerator is a polynomial of degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.
First and second order rational solutions to the Johnson equation and rogue waves
2018
Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.