This solution describes the soliton moving with the constant velocity and not changing the shape (modulus) of the Gaussian function. When a potential is added, not only can a single Gausson provide an exact solution to a number of cases of the Logarithmic Schrödinger equation, it has been found that a linear combination of Gaussons can very accurately approximate excited states as well. This superposition property of Gaussons has been demonstrated for quadratic potentials.