Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrödinger Equation

Abstract We consider the logarithmic Schrodinger equation (logNLS) in focusing regime. For this equation, Gaussian initial data remains Gaussian. In particular, Gausson - a time-independent function is an orbitally stable solution. paper, we construct multi-solitons (or multi-Gaussons) for logNLS, with estimates H 1 ? F ( ) . also solutions to logNLS behaving (in L 2 like sum of N different speeds (which call multi-gaussian). both cases, convergence (as t ? ? faster than exponential. prove rigidity result on these constructed multi-gaussians and multi-solitons, showing that they are only ones such convergence.