Generalized laplace transformations and integration of hyperbolic systems of linear partial differential equations

Abstract

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure generalizes the classical theory of Laplace transformations of second-order equations in the plane.

Laplace Transformation of Lie Class ω = 1 Overdetermined Systems

“…For recent advances of the factorization part we refer to [26] and to vast range of papers on differential Galois theory. But the transformation part has not seen much progress beside the classical second-order case (we refer for the development of the Darboux theory to [1][2][3]).…”

Метод Каскадного Интегрирования Лапласа Для Линейных Гиперболических Систем Уравнений

“…Во время подготовки настоящей публикации автору стало известно о работе [9], в которой предложена модификация каскадного метода интегрирования Лапласа для систем уравнений вида …”

On Factorization and Solution of Multidimensional Linear Partial Differential Equations

“…In this connection a generalization of Laplace invariants for higher-dimensional and higherorder cases started in [2], [21], [20], [17] would be of extreme importance. which made presentation of the results given above possible.…”

“…There were some attempts to generalize Laplace transformations for higherorder operators or larger number of independent variables, both in the classical time [12,15,16] and in the last decade [2,20]. A general definition of generalized factorization comprising all known practical methods was given in [19].…”