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...

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 ...

Fast nonlinear Fourier transform algorithms using higher order exponential integrators

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of highly accurate low-complexity algorithms remains a challenge. In this paper, we present new fast forward NFT...

Higher order exponential splittings for the fast Non-linear Fourier Transform of the Korteweg-De Vries equation

Non-linear Fourier Transforms (NFTs) enable the analysis of signals governed by certain non-linear evolution equations in a way that is analogous to how the conventional Fourier transform is used to analyse linear wave equations. Recently, fast numerical algorithms have been derived for the numerical computation of certain NFTs. In this paper,...

Conceptual framework for potential implementations of multicriteria decision making (MCDM) methods for design quality assesment

Architectural design can be considered as a process influenced by many stakeholders, each of which has different decision power. Each stakeholder might have his/her own criteria and weightings depending on his/her own perspective and role. Hence design can be seen as a multi-criteria decision making (MCDM) process. Considering architectural...

Conceptual framework for potential implementations of multi criteria decision making (MCDM) methods for design quality assessment

Architectural design can be considered as a process influenced by many stakeholders, each of which has different decision power. Each stakeholder might have his/her own criteria and weightings depending on his/her own perspective and role. Hence design can be seen as a multi-criteria decision making (MCDM) process. Considering architectural...

Conceptual framework for potential implementations of multi criteria decision making (MCDM) methods for design quality assessment

Architectural design can be considered as a process influenced by many stakeholders, each of which has different decision power. Each stakeholder might have his/her own criteria and weightings depending on his/her own perspective and role. Hence design can be seen as a multi-criteria decision making (MCDM) process. Considering architectural...