Abstract

In this paper we study ground-states of the Gierer & Meinhardt system on the line, namely solutions of the problem u? - u + v2/v = 0, ?-2v?-u + u2 = 0, u, v>0, u(±?) = 0 = v(±?). We prove that given any number N, there exists a solution to this problem exhibiting exactly N bumps in its u-component, separated from each other at a distance O(| log ?|), whenever ? is sufficiently small. These bumps resemble the shape of the unique solution of U? - U + U2 = 0, 0 < U(±?) = 0, U?(0) = 0. © World Scientific Publishing Company.