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This article is cited in 22 scientific papers (total in 22 papers)
Integrals, Solutions, and Existence Problems for Laplace Transformations of Linear Hyperbolic Systems
A. V. Zhibera, S. Ya. Startsevb a Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Abstract:
We generalize the notions of Laplace transformations and Laplace invariants for systems of hyperbolic equations and study conditions for their existence. We prove that a hyperbolic system admits the Laplace transformation if and only if there exists a matrix of rank $k$ mapping any vector whose components are functions of one of the independent variables into a solution of this system, where $k$ is the defect of the corresponding Laplace invariant. We show that a chain of Laplace invariants exists only if the hyperbolic system has a entire collection of integrals and the dual system has a entire collection of solutions depending on arbitrary functions. An example is given showing that these conditions are not sufficient for the existence of a Laplace transformation.
Received: 01.08.2002
Citation:
A. V. Zhiber, S. Ya. Startsev, “Integrals, Solutions, and Existence Problems for Laplace Transformations of Linear Hyperbolic Systems”, Mat. Zametki, 74:6 (2003), 848–857; Math. Notes, 74:6 (2003), 803–811
Linking options:
https://www.mathnet.ru/eng/mzm322https://doi.org/10.4213/mzm322 https://www.mathnet.ru/eng/mzm/v74/i6/p848
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