We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation in the super critical case i∂tu+14∂x4u=λ∂x(|u|ρ-1u), where ρ. >. 4, λ. ∈. C. We prove the global existence and the large time asymptotics of solutions for small initial data u0∈H1∩H12,1, when the order of the nonlinearity ρ. >. 4.
- Fourth-order nonlinear Schrödinger equation
- Large time asymptotics