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

Jing Wang, Na Xiong and Biao Li

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

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.

Date: 2019
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https://doi.org/10.1155/2019/1519305

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:1519305

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