We study the Cauchy problem for the nonlinear Klein-Gordon equation with a cubic convolution $\{V_{\gamma}*(w(t))^{2}\}w(t)$, where $V_{\gamma}(x)=|x|^{-\gamma}$, in $(x,t) \in \mathbf{R}^{n}\times \mathbf{R}$. We prove the existence of weak solutions for $0 \lt \gamma \lt$. We also prove that for $0\lt\gamma\lt{\rm Min}\{4, n\}$ the weak solution is unique and there exists a regular solution.

For a minimal immersion of a surface in a quaternionic Kähler manifold a concept of non-degeneracy is defined. Then using a theorem on elliptic differential systems we show a non-degenerate surface is in a sense generic, and around each point with possible exception of an isolated set of degenerate points we can define a smooth Darboux frame. The frame is continuous at a degenerate point. Next, by reducing the structure group we define a symmetric sextic form of type $(6,0)$ and we show in the case that ambient space is $HP^{n}$ this form is a holomorphic (abelian) differential. The last section is a brief note on the relation of our work to Glazebrook's twistor spaces for $HP^{n}$.