Objective The so-called integrable evolution equations possess several remarkable properties. In particular, their initial value problem can be solved using a nonlinear version of the Fourier transform method, called inverse scattering (spectral) method. For evolution equations in one and two spatial dimensions this method involves the Riemann-Hilbert and the d-bar formalisms, respectively.An important advantage of these formulations is that they can be used for the explicit evaluation of the long time behaviour of the solution. Among the most important integrable evolution equations in one space dimension is the Camassa-Holm (CH) equation, which is a certain generalization of the celebrated Korteweg-de Vries equation.The main objective of this project is to evaluate the long time behaviour of the solution of the CH equation using the Riemann-Hilbert formalism, to implement the inverse scattering method to equations analogous with the CH equation which are generalizations of the nonlinear Schroedinger and of the sine-Gordon equations, and to extend these results to integrable generalizations of the above equations in two and three spatial variables. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesphysical sciencesopticsfibre optics Keywords Camassa Camassa-Holm equation Holm equation Inverse Scattering Transform Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Topic(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Call for proposal FP6-2005-MOBILITY-5 See other projects for this call Funding Scheme EIF - Marie Curie actions-Intra-European Fellowships Coordinator THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE Address The old schools, trinity lane Cambridge United Kingdom See on map Links Website Opens in new window EU contribution No data
