Some aspects of a geometrical version of the Cauchy problem for the Hamilton-Jacobi equation are studied in the general framework of symplectic mechanics. The knowledge of a global complete solution allows us to solve explicitly generalized Cauchy problems by global solutions, here represented by Morse families generating Lagrangian manifolds. This leads in a natural way to a general version of Huygens' principle. © 1989 Società Italiana di Fisica.
ON THE GEOMETRICAL CAUCHY PROBLEM FOR THE HAMILTON-JACOBI EQUATION
CARDIN, FRANCO
1989
Abstract
Some aspects of a geometrical version of the Cauchy problem for the Hamilton-Jacobi equation are studied in the general framework of symplectic mechanics. The knowledge of a global complete solution allows us to solve explicitly generalized Cauchy problems by global solutions, here represented by Morse families generating Lagrangian manifolds. This leads in a natural way to a general version of Huygens' principle. © 1989 Società Italiana di Fisica.
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