Bäcklund Transformations for the One-Dimensional Schrödinger Equation

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Abstract

We study the system of equations which bases on the one-dimensionalSchrödinger equation and connects the potential, amplitude, and phase functions. Usingthe methods of compatibility theory of systems of partial differential equations, we obtain thecompletely integrable systems that connect only two functions of the above three. As a corollary,we construct some exact solutions of the Schrödinger equation.

Translated title of the contributionПреобразования бэклунда для одномерного уравнения Шрёдингера
Original languageEnglish
Pages (from-to)307-314
Number of pages8
JournalJournal of Applied and Industrial Mathematics
Volume15
Issue number2
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Bäcklund transformation
  • compatibility condition
  • Schrödinger equation

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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