arXiv subjects
Publications and source records attributed to Charles A. Miller.
A new parameterization of the Jacobi inversion problem is used along with the dynamics of the peaks to describe finite time interaction of peakon weak solutions of the Shallow Water equation.
The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.