Leiden University Scholarly Publications

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Westdorp, R.W.S. (2026)

Stochastic amplitude modulation of nonlinear dispersive waves

Doctoral Thesis
This dissertation investigates the propagation of solitary waves in the presence of random disturbances. We focus on paradigm models from nonlinear dispersive wave theory: the Korteweg–de Vries equation and the Fermi–Pasta–Ulam–Tsingou system. In both cases, random disturbances influence the wave amplitude. We develop a framework to track the evolution of the wave amplitude, yielding explicit predictions for its behavior, which we validate through numerical simulations. These results are supported by a rigorous analysis of wave stability.
Solitary waves
Korteweg- de Vries
Dispersion
SPDEs
FPUT lattice
All authors
Westdorp, R.W.S.
Supervisor
Hupkes, H.J.; Doelman, A.
Committee
Derks, G.; Jeu, M. de; MacLaurin, J.; Ambrose, D.M.; Roudenko, S.
Qualification
Doctor (dr.)
Awarding Institution
Mathematical Institute (MI), Faculty of Science, Leiden University
Date
2026-04-02
DOI
doi:10.60602/1887-4300492