Continuing our exploration of maximally supersymmetric gauge theories (MSYM) deformed by higher dimensional operators, in this paper we consider an off-shell approach based on pure spinor superspace and focus on constructing supersymmetric deformations beyond the first order. In particular, we give a construction of the Batalin-Vilkovisky action of an all-order non-Abelian Born-Infeld deformation of MSYM in the non-minimal pure spinor formalism. We also discuss subtleties in the integration over the pure spinor superspace and the relevance of Berkovits-Nekrasov regularization.

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Motivated by the paper of Beals, Sattinger and Szmigielski (2000) [3], we propose an extension of the CamassaHolm equation, which also admits the multipeakon solutions. The novel aspect is that our approach is mainly based on classic determinant technique. Furthermore, the proposed equation is shown to possess a nonisospectral Lax pair.