Kink Soliton Solutions in the Logarithmic Schrödinger Equation

We re-examine the mathematical properties of the kink and antikink soliton solutions to the Logarithmic Schrödinger Equation (LogSE), a nonlinear logarithmic version of the Schrödinger Equation incorporating Everett–Hirschman entropy. We devise successive approximations with increasing accuracy. From the most successful forms, we formulate an analytical solution that provides a very accurate solution to the LogSE. Finally, we consider combinations of such solutions to mathematically model kink and antikink bound states, which can serve as a possible candidate for modeling dilatonic quantum gravity states.