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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 1(337), Pages 63–106 (Mi umn357)  

This article is cited in 114 scientific papers (total in 114 papers)

Exactly integrable hyperbolic equations of Liouville type

A. V. Zhibera, V. V. Sokolovb

a Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
b Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Abstract: This is a survey of the authors' results concerning non-linear hyperbolic equations of Liouville type. The definition is based on the condition that the chain of Laplace invariants of the linearized equation be two-way finite. New results include a procedure for finding the general solution and a solution of the classification problem for Liouville type equations.

DOI: https://doi.org/10.4213/rm357

Full text: PDF file (438 kB)
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English version:
Russian Mathematical Surveys, 2001, 56:1, 61–101

Bibliographic databases:

UDC: 517.957+514.85
MSC: Primary 35L70; Secondary 35A22, 35A30, 35L75, 35Q53, 37K10, 37K35, 37J15, 3
Received: 20.08.2000

Citation: A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Uspekhi Mat. Nauk, 56:1(337) (2001), 63–106; Russian Math. Surveys, 56:1 (2001), 61–101

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