PreprintArticleVersion 2Preserved in Portico This version is not peer-reviewed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)
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. Physics2021, 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.
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. Physics2021, 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.
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
Subject
Physical Sciences, Condensed Matter Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Michael Tribelsky
Commenter's Conflict of Interests: Author