1 Introduction: higher-order evolution models, self-similar blow-up, compactons, and standing wave so-lutions

Thus, we describe common local and global properties of weak compactly supported solutions of nonlinear partial differential equations (PDEs):

(I) 2mth-order quasilinear parabolic PDEs with regional blow-up,

(II) 2mth-order quasilinear hyperbolic PDEs with regional blow-up,

(III) (2m+1)th-order NDEs with TW compactons, and

(IV) 2mth-order quasilinear Schro¨dinger equations with periodic standing wave solutions.