Non-existence conjecture for regular solutions of the system $\mathcal{E}^{\gamma,\delta}_{k,\ell}$

Let $\gamma$ and $\delta$ be real analytic functions with $\gamma_4\neq0$, let $k$ and $\ell$ be integers, and let $\mathcal{E}^{\gamma,\delta}_{k,\ell}$ denote the partial differential system defined in. A non-existence conjecture for regular solutions. For any such $\gamma$, $\delta$, $k$, and $\ell$, the system $\mathcal{E}^{\gamma,\delta}_{k,\ell}$ does not admit any regular solution $p$. This claim concerns the non-existence of regular solutions for a broad class of real analytic systems; the supplied text gives no evidence that the claim has been proved or disproved.