Peakon Solutions of Alice-Bob b-Family Equation and Novikov Equation

Abstract EN

By requiring B=P^sT^dA and substituting u=A+B into the b-family equation and Novikov equation, we can obtain Alice-Bob peakon systems, where P^s and T^d are the arbitrary shifted parity transformation and delayed time reversal transformation, respectively.

The nonlocal integrable Camassa-Holm equation and Degasperis-Procesi equation can be derived from the Alice-Bob b-family equations by choosing different parameters.

Some new types of interesting solutions are solved including explicit one-peakons, two-peakons, and N-peakons solutions.