On the generation of equivalent Hamiltonians

What is it about?

new approach to the equivalence problem (in phase space) is presented. Given a Hamiltonian describing a system of particles with two degrees of freedom (and the corresponding Hamilton–Jacobi equation), it is shown how to find the most general family of Hamiltonian functions that generates a new Hamilton–Jacobi equation with the following (and essential) characteristic, here defined as equivalence: Every new solution is also a solution of the original Hamilton–Jacobi equation and vice versa.

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Why is it important?

The equivalence generated by a family of Hamiltonian functions between the Hamilton-Jacobi equations giving alternative ways for solution of this nonlinear partial differential equations.