Kink Soliton Solutions in the Logarithmic Schrödinger Equation

What is it about?

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.

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Photo by Kobby Mendez on Unsplash

Photo by Kobby Mendez on Unsplash

Why is it important?

We found relatively simple analytical solutions that accurately approximate the kink and antikink soliton solutions of the LogSE. The LogSE serves as a good model for the Higgs potential. Because the log term of the LogSE is not Lipschitz continuous when the wave function is zero, that produces an "élan" or self-excitation that could be responsible for the spontaneous symmetry breaking phenomenon.

Perspectives