# Peakon Solutions of Alice-Bobb-Family Equation and Novikov Equation

Authors: Jing Wang; Na Xiong; Biao Li
Journal: Advances in Mathematical Physics
 (2019)

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## Abstract

By requiringB=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.


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## Body


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*Source: 1519305-2019-05-02.xml*