Mapping of solutions of the Hamilton-Jacobi equation by an arbitrary canonical transformation
G.F. Torres del Castillo, H.H. Cruz Dom\'inguez, A. de Yta, Hern\'andez, J.E. Herrera Flores, and A. Sierra Mart\'inez
TL;DR
The paper demonstrates a general method for transforming solutions of the Hamilton-Jacobi equation under any canonical transformation, providing a systematic way to generate new solutions from existing ones.
Contribution
It introduces a natural mapping that relates solutions of the Hamilton-Jacobi equation before and after an arbitrary canonical transformation.
Findings
Mapping preserves solutions of the Hamilton-Jacobi equation
Applicable to any Hamiltonian and canonical transformation
Facilitates solution generation in Hamiltonian mechanics
Abstract
It is shown that given an arbitrary canonical transformation and an arbitrary Hamiltonian, there is a naturally defined mapping that sends any solution of the Hamilton-Jacobi (HJ) equation into a solution of the HJ equation corresponding to the new Hamiltonian
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Waves and Solitons · Nonlinear Dynamics and Pattern Formation