Stability of standing waves for logarithmic Schrödinger equation with attractive delta potential

Abstract

We consider the one-dimensional logarithmic Schrödinger equation with a delta potential. Global well-posedness is verified for the Cauchy problem in H1(R) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach.

24 pages

References in corpus (2)

• Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
• Fast soliton scattering by delta impurities