Singular Perturbation of Solitons
Long wavelength perturbation theory is at the heart of many physical approximations. It amounts to neglect derivatives and nonlinearities of higher orders, in a rational expansion. However, it may happen, that, this is formally consistent; yet the ensuing series is diverging, and so one has to investigate what really happens beyond all algebraic orders. Below, I look at a particular example of this situation, i. e. to the robustness of soliton-like solutions of the Korteweg-de Vries equation when higher order derivatives with respect to the space variable are included. This is an abridged version of a joint work with Alfred Ramani and Basile Grammaticos .
KeywordsTravel Wave Solution Logarithmic Singularity Shallow Water Wave Stokes Line Abridge Version
Unable to display preview. Download preview PDF.