摘 要: |
As non-smooth solitons, peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. One natural concept of peakons is dictated by the distributional compatibility of the Lax pairs. Due to the Lax integrability, the inverse spectral method is a powerful tool for the study of these solutions. This talk particularly focuses on related results for the Novikov equation, including distributional Lax integrability, orthogonality, forward and inverse spectral problems, global existence and large time asymptotic behaviors, etc. |