What is Gausson (physics)?

The Gausson is a soliton which is the solution of the logarithmic Schrödinger equation, which describes a quantum particle in a possible nonlinear quantum mechanics. The logarithmic Schrödinger equation preservesthe dimensional homogeneity of the equation, i.e. the product of the independent solutions in one dimension remain the solution in multiple dimensions.While the nonlinearity alone cannot cause the quantum entanglement between dimensions, the logarithmic Schrödinger equation can be solved by the separation of variables.

Let the nonlinear Logarithmic Schrödinger equation in one dimension will be given by {\displaystyle } :

Let assume the Galilean invariance i.e.

Substituting