Bäcklund Transformations for the One-Dimensional Schrödinger Equation

Standard

Bäcklund Transformations for the One-Dimensional Schrödinger Equation. / Neshchadim, M. V.

In: Journal of Applied and Industrial Mathematics, Vol. 15, No. 2, 04.2021, p. 307-314.

Research output: Contribution to journal › Article › peer-review

Harvard

Neshchadim, MV 2021, 'Bäcklund Transformations for the One-Dimensional Schrödinger Equation', Journal of Applied and Industrial Mathematics, vol. 15, no. 2, pp. 307-314. https://doi.org/10.1134/S1990478921020125

APA

Neshchadim, M. V. (2021). Bäcklund Transformations for the One-Dimensional Schrödinger Equation. Journal of Applied and Industrial Mathematics, 15(2), 307-314. https://doi.org/10.1134/S1990478921020125

Vancouver

Neshchadim MV. Bäcklund Transformations for the One-Dimensional Schrödinger Equation. Journal of Applied and Industrial Mathematics. 2021 Apr;15(2):307-314. doi: 10.1134/S1990478921020125

Author

Neshchadim, M. V. / Bäcklund Transformations for the One-Dimensional Schrödinger Equation. In: Journal of Applied and Industrial Mathematics. 2021 ; Vol. 15, No. 2. pp. 307-314.

BibTeX

@article{670afd88379b44f68f2022938a861f29,

title = "B{\"a}cklund Transformations for the One-Dimensional Schr{\"o}dinger Equation",

abstract = "We study the system of equations which bases on the one-dimensionalSchr{\"o}dinger 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 Schr{\"o}dinger equation.",

keywords = "B{\"a}cklund transformation, compatibility condition, Schr{\"o}dinger equation",

author = "Neshchadim, {M. V.}",

note = "Funding Information: The author was supported by the State Task of the Sobolev Institute of Mathematics (project no. 0314–2019–0011). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = apr,

doi = "10.1134/S1990478921020125",

language = "English",

volume = "15",

pages = "307--314",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Bäcklund Transformations for the One-Dimensional Schrödinger Equation

AU - Neshchadim, M. V.

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Bäcklund transformation

KW - compatibility condition

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85116236772&partnerID=8YFLogxK

U2 - 10.1134/S1990478921020125

DO - 10.1134/S1990478921020125

M3 - Article

AN - SCOPUS:85116236772

VL - 15

SP - 307

EP - 314

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 34401070