When Do JONSWAP Spectra Lead to Soliton Gases in Deep Water Conditions?

When a large number of solitons dominates the dynamics of a system, scientists describe this collective behaviour of solitons as a soliton gas. Soliton gases are currently the subject of intense practical and theoretical investigations. The existence of soliton gases has been confirmed in experiments, but is not clear what kind of sea states...

Fast and Reliable Detection of Significant Solitons in Signals with Large Time-Bandwidth Products

We present a fast method to calculate the significantly large solitonic components of signals with large time-bandwidth products governed by the nonlinear Schrödinger equation, for which the computation typically becomes prohibitively expensive and/or numerically unstable. We partition the full signal in both frequency and time to obtain...

Fast Single-Mode Fiber Nonlinearity Monitoring: An Experimental Comparison Between Split-Step and Nonlinear Fourier Transform-Based Methods

We experimentally investigate the problem of monitoring the Kerr-nonlinearity coefficient $\gamma$ from transmitted and received data for a single-mode fiber link of 1600 km length. We compare the accuracy and speed of three different approaches. First, a standard split-step Fourier method is used to predict the output at various $\gamma$...

Orbital Stability of Patterns in Semilinear SPDE using a Multiscale Analysis

In this thesis we consider orbital stability of certain patterns in stochastic partial differential equations. We study two examples: a rotating wave in a two-dimensional reaction-diffusion equation and a soliton in a parametrically forced nonlinear Schrödinger equation. In both cases, we show that, for small noise, solutions to the stochastic...

Modelling wave propagation over a current in a stratified fluid

Layman Summary<br/>The goal of this paper is to study how waves move over a fluid in with an underlying current. Oceans displace debris and heat. Ocean models can be used to predict the movement of debris and even predict the effect of the movements of oceans on the climate. Modeling water can be improved by introducing more information from...

Reliable numerical algorithms for the Non-linear Fourier Transform of the KdV equation

<b>Research question</b><br/>The topic of this dissertation is the numerical computation of the forward and inverse Non-linear Fourier Transform (NFT) for the Korteweg–de Vries equation (KdV), for sampled signals that decay sufficiently fast on both sides. With NFTs certain non-linear Partial Differential Equations (PDEs) can be solved in a way...

Comparative analysis of bore propagation over long distances using conventional linear and KdV-based nonlinear Fourier transform

In this paper, we study the propagation of bores over a long distance. We employ experimental data as input for numerical simulations using COULWAVE. The experimental flume is extended numerically to an effective relative length of x/h=3000, which allows all far-field solitons to emerge from the undular bore in the simulation data. We apply the...

Experimental validation of nonlinear Fourier transform-based Kerr-nonlinearity identification over a 1600km SSMF link

Recently, a nonlinear Fourier transform-based Kerr-nonlinearity identification algorithm was demonstrated for a 1000 km NZDSF link with accuracy of 75%. Here, we demonstrate an accuracy of 99% over 1600 km SSMF. Reasons for improved accuracy are discussed.

Analysis of Bore Characteristics Using KdV-Based Nonlinear Fourier Transform

Bores propagating in shallow water transform into undular bores and, finally, into trains of solitons. The observed number and height of these undulations, and later discrete solitons, is strongly dependent on the propagation length of the bore. Empirical results show that the final height of the leading soliton in the far-field is twice the...

Soliton Interpretation of Arterial Blood Pressure Waveform: Derivation, Verification of Korteweg-de Vries type Dynamics and Application of Nonlinear Fourier Analysis

As a nonlinear alternative to the linear interpretation of arterial blood pressure waveform, soliton theory has been proposed to model arterial blood pressure by interpreting the pulsatile nature of pressure pulses in the viewpoint of soliton transmission. The existing solitary wave literature supports this interpretation by deriving Korteweg-de...

Soliton phase shift calculation for the Korteweg–de Vries equation

Several non-linear fluid mechanical processes, such as wave propagation in shallow water, are known to generate solitons: localized waves of translation. Solitons are often hidden in a wave packet at the beginning and only reveal themselves in the far-field. With a special signal processing technique known as the non-linear Fourier transform ...

Improved Fast Inverse Nonlinear Fourier Transform for Multi-solitons: A Discrete Darboux Based Approach

The relation between the input of an ideal optical single-mode fiber and the corresponding fiber output constitutes a nonlinear system that can be described using the nonlinear Schrödinger equation. This nonlinear system has the interesting property that it can be solved analytically using nonlinear Fourier transforms. To utilize this property,...

Discrete Darboux based fast inverse nonlinear Fourier transform algorithm for multi-solitons

A fast algorithm for constructing multi-solitons with linear complexity in the number of samples and eigenvalues is introduced. The algorithm is shown to be significantly faster than the conventional Darboux transform in a numerical example, with acceptable error.

Numerical modelling of solitary internal waves in the Browse Basin.

Shell is developing a floating liquefied natural gas (FLNG) facility to extract and process natural gas in the Browse Basin on the North West Shelf of Australia. This shelf break area is known for its strong tidal currents and year-round stratification. Tidal currents transporting stratified water over steep bathymetry can generate large...

Solitons and nonlinear dispersive waves

Description of a mathematical model to describe solitons in matlab.