Travelling wave solutions to a gradient system

James F. Reineck
1988 Transactions of the American Mathematical Society  
Given a system of reaction-diffusion equations where the nonlinearity is derived from a potential with certain restrictions, we use the Conley index and the connection matrix to show that there is a travelling wave solution connecting the maxima of the potential.
doi:10.1090/s0002-9947-1988-0940216-8 fatcat:oghlik27t5dpxp74nsghkqiqse