Existence and orbital stability of standing waves for the 1D Schrödinger-Kirchhoff equation

Abstract: In this paper we establish the orbital stability of standing wave solutions associated to the one-dimensional Schr\"odinger-Kirchhoff equation. The presence of a mixed term gives us more dispersion, and consequently, a different scenario for the stability of solitary waves in contrast with the corresponding nonlinear Schr\"odinger equation. For periodic waves, we exhibit two explicit solutions and prove the orbital stability in the energy space.