On some nonlinear equations generated by Fueter type operators (Q1340785)

Summary: Let \(\mathbb{H}(\mathbb{C})\) be the set of complex quaternions, \(i_ k\) the standard basic quaternions and, for \(q\in \mathbb{H}(\mathbb{C})\), denote \(\vec q= \sum_{k=1}^ 3 q_ k i_ k\) and \(\overline{q}= q_ 0- \vec q\). In the present work some procedure of factorization with reference to the Fueter type equations \((\partial_ t- aD)u=0\) for \(u= u(t,x)\) where \(D= \sum_{k=1}^ 3 i_ k {\partial \over {\partial x_ k}}\) is discussed.