Hamiltonians of the Generalized Nonlinear Schrödinger Equations

Nikolay A. Kudryashov ()
Additional contact information
Nikolay A. Kudryashov: Moscow Engineering Physics Institute, National Research Nuclear University MEPhI, 31 Kashirskoe Shosse, 115409 Moscow, Russia

Mathematics, 2023, vol. 11, issue 10, 1-12

Abstract: Some types of the generalized nonlinear Schrödinger equation of the second, fourth and sixth order are considered. The Cauchy problem for equations in the general case cannot be solved by the inverse scattering transform. The main objective of this paper is to find the conservation laws of the equations using their transformations. The algorithmic method for finding Hamiltonians of some equations is presented. This approach allows us to look for Hamiltonians without the derivative operator and it can be applied with the aid of programmes of symbolic calculations. The Hamiltonians of three types of the generalized nonlinear Schrödinger equation are found. Examples of Hamiltonians for some equations are presented.

Keywords: nonlinear Schrödinger equation; Hamiltonian; conservation law; optical soliton; conservative quantity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/10/2304/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/10/2304/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:10:p:2304-:d:1147469

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().