Compactification of Nonlinear Patterns and Waves

We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [Phi'(u(x))](x) = P'(u) equation, where Phi'(sigma) = sigma + beta sigma(3) and endowed with a subquadratic site potential P(u) similar to vertical bar 1 - u(2)vertical bar(alpha+1), 0 <= alpha < 1, and the Schrodinger iZ(t) + del(2)Z = G(vertical bar Z vertical bar)Z equation in a plane with G(A) = gamma A(-delta) - sigma A(2), 0 < delta <= 1.