Kink Soliton Solutions in the Logarithmic Schrödinger Equation

Tony C. Scott () and M. Lawrence Glasser
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Tony C. Scott: Institut für Physikalische Chemie, RWTH Aachen University, 52056 Aachen, Germany
M. Lawrence Glasser: Department of Physics, Clarkson University, Potsdam, NY 13676, USA

Mathematics, 2025, vol. 13, issue 5, 1-12

Abstract: 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.

Keywords: logarithmic Schrödinger equation; kink soliton; Everett–Hirschman entropy; nonlinear differential equations; computer algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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