Infinitely many nonlocal conservation laws for the ABC equation with \(A+B+C\ne 0\)

  • I. S. Krasil’shchik
  • A. Sergyeyev
  • O. I. Morozov


We construct an infinite hierarchy of nonlocal conservation laws for the ABC equation \(A u_t\,u_{xy}+B u_x\,u_{ty}+C u_y\,u_{tx} = 0\), where ABC are nonzero constants and \(A+B+C\ne 0\), using a nonisospectral Lax pair. As a byproduct, we present new coverings for the equation in question. The method of proof of nontriviality of the conservation laws under study is quite general and can be applied to many other integrable multidimensional systems.

Mathematics Subject Classification

37K05 37K10 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • I. S. Krasil’shchik
    • 1
    • 2
  • A. Sergyeyev
    • 3
  • O. I. Morozov
    • 4
  1. 1.Independent University of MoscowMoscowRussia
  2. 2.Russian State University for the HumanitiesMoscowRussia
  3. 3.Mathematical InstituteSilesian University in OpavaOpavaCzech Republic
  4. 4.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland

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