Traveling wave solutions of a gradient system: solutions with a prescribed winding number. II

This paper completes the analysis begun in [2] concerning the existence of traveling wave solutions of a system of the form ${u_t} = {u_{xx}} + \nabla F(u)$, $u \in {{\mathbf{R}}^2}$. In [2] a notion of winding number for solutions was defined, and the proof that there exists a traveling wave solution with a prescribed winding number was reduced to a purely algebraic problem. In this paper the algebraic problem is solved.