Variational Statement of the Schrödinger Equation with a Nonstationary Nonlinearity and Its Integrals of Motion

The inverse variational problem is solved for the nonlocal nonlinear Schrödinger equation modeling filamentation processes in various nonlinear media. The corresponding integral relations generalizing conservation laws to the nonconservative case are obtained.

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Bibliographic Details
Published inDifferential equations Vol. 54; no. 10; pp. 1394 - 1398
Main Authors Bulygin, A. D., Zemlyanov, A. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2018
Springer
Springer Nature B.V
Subjects
Conservation laws
Difference and Functional Equations
Differential equations
Integrals
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Schrodinger equation
Short Communications
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Summary:The inverse variational problem is solved for the nonlocal nonlinear Schrödinger equation modeling filamentation processes in various nonlinear media. The corresponding integral relations generalizing conservation laws to the nonconservative case are obtained.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266118100105