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TMF, 2015, Volume 183, Number 3, Pages 372–387 (Mi tmf8820)  

This article is cited in 7 scientific papers (total in 7 papers)

Bäcklund transformations relating different Hamilton–Jacobi equations

A. P. Sozonov, A. V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia

Abstract: We discuss one of the possible finite-dimensional analogues of the general Bäcklund transformation relating different partial differential equations. We show that different Hamilton–Jacobi equations can be obtained from the same Lax matrix. We consider Hénon–Heiles systems on the plane, Neumann and Chaplygin systems on the sphere, and two integrable systems with velocity-dependent potentials as examples.

Keywords: general Bäcklund transformation, Hamilton–Jacobi equation, separation of variables, Lax matrix

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00061
Saint Petersburg State University 11.38.664.2013


DOI: https://doi.org/10.4213/tmf8820

Full text: PDF file (461 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2015, 183:3, 768–781

Bibliographic databases:

PACS: 02.90.+p, 03.40.Kf
MSC: 58J72, 70H06
Received: 17.11.2014
Revised: 10.01.2015

Citation: A. P. Sozonov, A. V. Tsiganov, “Bäcklund transformations relating different Hamilton–Jacobi equations”, TMF, 183:3 (2015), 372–387; Theoret. and Math. Phys., 183:3 (2015), 768–781

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v183/i3/p372

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Tsiganov, “Two integrable systems with integrals of motion of degree four”, Theoret. and Math. Phys., 186:3 (2016), 383–394  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. V. Tsiganov, “Abel's theorem and Bäcklund transformations for the Hamilton–Jacobi equations”, Proc. Steklov Inst. Math., 295 (2016), 243–273  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Yu. A. Grigorev, A. P. Sozonov, A. V. Tsyganov, “Ob odnoi integriruemoi sisteme na ploskosti s potentsialom, zavisyaschim ot skorosti”, Nelineinaya dinam., 12:3 (2016), 355–367  mathnet  crossref  mathscinet  elib
    4. Andrey V. Tsiganov, “Bäcklund Transformations for the Nonholonomic Veselova System”, Regul. Chaotic Dyn., 22:2 (2017), 163–179  mathnet  crossref
    5. A. V. Tsyganov, “Ob odnoi integriruemoi sisteme na ploskosti s integralom dvizheniya shestoi stepeni po impulsam”, Nelineinaya dinam., 13:1 (2017), 117–127  mathnet  crossref  elib
    6. A. V. Tsiganov, “Bäcklund transformations for the Jacobi system on an ellipsoid”, Theoret. and Math. Phys., 192:3 (2017), 1350–1364  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. A. V. Tsiganov, “New bi-Hamiltonian systems on the plane”, J. Math. Phys., 58:6 (2017), 062901  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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