Solutions of nonlinear equations of divergence type in domains having corner points

Perepelkin, E. E.; Садовников, Б. И.; Иноземцева, Н. Г.

doi:10.1007/s41808-018-0013-6

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Cited by 2 publications

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“…As a result, the problem is reduced to a non-linear partial differential equation for the phase of the wave function. Using the non-linear Legendre transform [15][16][17], we reduce the non-linear equation to a linear partial differential equation. Particular solutions of such an equation can be found by the separation of variables method.…”

Section: Introductionmentioning

confidence: 99%

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A new class of exact solutions of the Schrödinger equation

Perepelkin

Садовников

Иноземцева

et al. 2018

Continuum Mech. Thermodyn.

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The aim of this paper is to find the exact solutions of the Schrödinger equation. As is known, the Schrödinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of continuity is linearized. Particular solutions of such a linear equation are found in the paper and an inverse Legendre transform is considered for them with subsequent construction of solutions of the Schrödinger equation. Examples of the classical and quantum systems are considered.

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Section: Introductionmentioning

confidence: 99%

“…Let us assume that there is no vortex flow In this case the phase  of the wave function  is a harmonic function.If the condition (1.12) is not satisfied, then it is necessary to solve the non-linear equation(1.11). For the equation (1.11) to be linearized, let us use the Legendre transform[15][16][17]…”

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confidence: 99%