In memory of Mikhail Aleksandrovich El'yashevich

Aleksandrov, E. B.; Алферов, Жорес Иванович; Апанасевич, П. А.; Bonch-Bruevich, A M; Borisevich, N A; Burakov, V S; Goldanskii, V. I.; Voitovich, A P; Грибов, Л. А.; Martynenko, O M; Min'ko, L Ya; Tomil'chik, L M; Chernyavskii, A F

doi:10.1070/pu1996v039n08abeh001528

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2021

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“…In other words, it means that E (0) ξ (ξ) is an eigenfunction of the stability problem with zero eigenvalue. Note that we obtain this result based on the translational invariance solely, without the employment of a specific form of the differential operator in Equation (2). These neutrallystable modes generated by a transformation of a continuous group of symmetry are called Goldstone modes.…”

Section: Stability Analysismentioning

confidence: 89%

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

Tribelsky

2021

Physics

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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 the 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.

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Section: Stability Analysismentioning

confidence: 89%

“…Now, Minsk is the capital of independent state Belarus, while, at that time, Minsk and Moscow both belonged to a single state: the Soviet Union. In Minsk, I met my first scientific adviser Mikhail Aleksandrovich El'yashevich [2].…”

Section: Historical Remarksmentioning

confidence: 99%

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

Tribelsky

2021

Physics

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In memory of Mikhail Aleksandrovich El'yashevich

Cited by 1 publication

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

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

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