On the extended crystal PDE's stability. I: The n-d'Alembert extended crystal PDE's

Our recent results on extended crystal PDE's and geometric theory on PDE's stability, are applied to the generalized n-d'Alembert PDE's, (d′A)n, n⩾2. We prove that these are extended crystal PDE's for any n⩾2. For suitable n, (d′A)n becomes an extended 0-crystal PDE and also a 0-crystal PDE. An equation, having all the same smooth solutions of (d′A)n, but without unstabilities at “finite time” is obtained for each n⩾2.