Finite traveling waves for a nonlinear degenerate reaction-diffusion system (Q1570958)

The author studies the existence of finite traveling waves (\(u_i(x,t)=u_i(z)\), with \(z=x+c t\) and \(c\) the speed) to the nonlinear degenerate reaction--diffusion system \[ (u_i^{\alpha_i})_t = u_{ixx} - \prod_{j=1}^{N}{u_j^{m_{ij}}}, \quad x \in {\mathbb{R}}, \quad t >0, i=1, \dots,N, \] with \(\alpha_i>0\), \(m_{ij}\geq 0\) and \(\sum_{j=1}^{N}{m_{ij}} >0\). Translating this equation to an equivalent one, he obtains existence results in function of the sign of \(c\).