| Abstract: |
| A class of nonlinear integrable PDEs admit some special weak solutions called ``peakons'', which are characterised by ODE systems, namely peakon lattices. The celebrated Toda lattice was originally obtained as a simple model for describing a chain of particles with nearest neighbor exponential interaction. For some initial value problems, these lattices can be explicitly solved by use of inverse spectral method involving certain continued fractions, which also associate with some "orthogonality". In this talk, I will take Camassa-Holm(CH) peakon & Toda lattices & ordinary orthogonal polynomials (OPs), 2-component modified CH interlacing peakon & Kac-van Moerbeke lattices & symmetric OPs, Novikov peakon & B-Toda lattices & Partial skew OPs, Degasperis-Procesi peakon & C-Toda lattices & Cauchy Bi-OPs, as examples to illustrate these connections. Some of the results comes from my recent works with Xing-Biao Hu, Yi He, Shi-Hao Li, Jacek Szmigielski and Jun-Xiao Zhao. |
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