infinite dimensional hamiltonian systeminfinite dimensional hamiltonian systemAn infinite dimensional Hamiltonian system takes the form(IHS){∂tu-Δxu=Hv(t,x,u,v)-∂tv-Δxv=Hu(t,x,u,v)∀(t,x)∈ℝ×Ωwhere Ω⊂ℝN is a smoothly bounded domain,H∈𝒞1(ℝ×Ω¯×ℝ2,ℝ).