Abstract
For a Cauchy—Kovalevskaya system of linear homogeneous first-order partial differential equations defined by constant matrices multiplying the derivatives, we construct a wave interaction model. The elements of the model include traveling waves containing the matrix coefficients of the system, the wave interaction operators defined on traveling waves, and the operator exponential corresponding to the system. The general solution of the system is represented as an expansion in traveling waves, and the Cauchy problem is considered for the series expansion of an analytic initial function in the initial states of the corresponding wave interaction operators.
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Original Russian Text © V.V. Feoktistov, O.O. Myakinnik, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 8, pp. 1083–1095.
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Feoktistov, V.V., Myakinnik, O.O. Wave interaction model for a Cauchy—Kovalevskaya system of first-order partial differential equations with constant coefficients. Diff Equat 51, 1079–1091 (2015). https://doi.org/10.1134/S0012266115080121
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DOI: https://doi.org/10.1134/S0012266115080121