The Fourth-order dispersive nonlinear Schrödinger equation: orbital stability of a standing wave

Abstract

Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.

To appear in SIADS

References in corpus (1)

• Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case