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

Author:

Wang Jing1,Xiong Na2,Li Biao1ORCID

Affiliation:

1. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China

2. College of Science and Technology, Ningbo University, Ningbo 315211, China

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

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