We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

Perturbed KdV equations and their integrability properties

TER-BRAAK, FLORIS (2018) Perturbed KdV equations and their integrability properties. Doctoral thesis, Durham University.

PDF - Accepted Version


In this thesis we investigate the integrability properties of the regularized long-wave (RLW) equation and modified regularized long-wave (mRLW) equation as perturbations of the integrable Korteweg-de Vries (KdV) equation. We study various properties of numerical mRLW three-soliton scattering and compare these with the corresponding RLW soliton solutions. We find that the numerical mRLW solitons behave much like integrable solitons in the sense that the only result of the three-soliton interaction is the phase shift each soliton experiences, which is approximately equal to the sum of pairwise phase shifts. Furthermore, we investigate the so-called quasi-integrability properties of these RLW and mRLW simulations. Using both analytical and numerical methods, we argue that these models possess an infinite amount of asymptotically conserved charges, i.e., quasi-conserved charges, which are observed in multi-soliton interactions. Finally, we also simulate numerical RLW and mRLW solutions in the presence of additional perturbing terms. This allows us to study soliton-radiation interactions and we find that for certain perturbations, these interactions preserve the quasi-conservation laws to a certain extend.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Keywords:integrability, quasi-integrability
Faculty and Department:Faculty of Science > Mathematical Sciences, Department of
Thesis Date:2018
Copyright:Copyright of this thesis is held by the author
Deposited On:19 Apr 2018 11:50

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter