Generic transversality of travelling fronts, standing fronts, and standing pulses for parabolic gradient systems

Romain Joly, Emmanuel Risler

For nonlinear parabolic systems of the form \[ \partial_t w(x,t) = \partial_{x}^2 w(x,t) - \nabla V\bigl(w(x,t)\bigr) \,, \] the following conclusions are proved to hold genericall…