Anti-phase Travelling Waves In FPU Lattices

In this paper we discuss in FPU lattices the existence of travelling wavesolutions with adjacent particles having anti-phase hull functions. We studythis problem via variational method, that is, we apply the linking theorem orthe saddle-point theorem to show the existence of anti-phase travelling wavesolutions in different situations. We convert a travelling wave solution to aperiodic solution of an advance-delay differential equation. Then we define aC~1functional in a suitable function space. If this functional has a criticalpoint, then this critical point corresponds to a periodic solution of theadvance-delay differential equation. Finally, applying the linking theorem andthe saddle-point theorem, we show the existence of critical points, leading tothe existence conclusions of anti-phase travelling wave solutions.