Peakon Solutions of Alice-Bob - Family Equation and Novikov Equation
Biao Li (),
Jing Wang () and
Na Xiong ()
Advances in Mathematical Physics, 2019, vol. 2019, 1-8
By requiring and substituting into the - family equation and Novikov equation, we can obtain Alice-Bob peakon systems, where and 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 - family equations by choosing different parameters. Some new types of interesting solutions are solved including explicit one-peakons, two-peakons, and - peakons solutions.
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