Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Schrödinger Equation with Complicated Potential

Version 1 : Received: 14 July 2021 / Approved: 15 July 2021 / Online: 15 July 2021 (09:38:02 CEST)
Version 2 : Received: 6 August 2021 / Approved: 6 August 2021 / Online: 6 August 2021 (14:15:43 CEST)
(This article belongs to the Research Topic Quantum Computing)

A peer-reviewed article of this Preprint also exists.

Tribelsky, M.I. Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Schrödinger Equation with Complicated Potential. Physics 2021, 3, 715-727. Tribelsky, M.I. Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Schrödinger Equation with Complicated Potential. Physics 2021, 3, 715-727.

Journal reference: Physics 2021, 3, 43
DOI: 10.3390/physics3030043

Abstract

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

Keywords

nonlinear diffusion; traveling waves; stability; Goldstone modes; Shrödinger equation; spectrum of low-exited states

Comments (1)

Comment 1
Received: 6 August 2021
Commenter: Michael Tribelsky
Commenter's Conflict of Interests: Author
Comment: Modifications in response to the reports of the Reviewers
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