On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system

Abstract

We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as a special case of a two-component peakon system (exhibiting a cubic nonlinearity), we convert the Cauchy problem into a system of ordinary differential equations in a Banach space. Using this approach, we are able to demonstrate local well-posedness in the Sobolev space $H^s$ where $s>5/2$. We also establish the continuity properties for the data-to-solution map for a range of Sobolev spaces. Finally, we briefly explore the relationship between the two-component system and the bi-Hamiltonian AKNS hierarchy.

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Cited by in corpus (1)

• On the well-posedness of the Cauchy problem for the two-component peakon system in $C^k\cap W^{k,1}$