Blow-up of the solution of a nonlinear Schrödinger equation system with periodic boundary conditions - Ivanauskas, Feliksas; Puriuškis, Gintaras (Nonlinear Analysis: Modelling and Control, 2013)
We consider a system of nonlinear Schrödinger equations with periodic boundary conditions of the formi ∂uj/∂t + D2uj = −fj (u, ū),    t ≥ 0,  x ∈ (−2,2),uj (0, x) = uj0(x),    x ∈ (−2,2),Dkuj (t, −2) = Dkuj (t, 2),     t ≥ 0,   k = 0, 1,where D = ∂/∂x,  j = 1,..., m,  fj (u, ū) = ∂g(u, ū)/∂ū, and ∂g/∂uj = –f j for some homogenous function g(u, ū) such that g(λu, λū) = λ6g(u, ū). We obtain sufficient conditions for blow-up of solutions of this system in C1([0,t0);H2(−2,2)).