Lagrangian, Hamiltonian and other Structures for the Heat Equation and Potential Burgers Equation

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dc.creatorBustamante, Miguel D.
dc.creatorHojman, Sergio A.
dc.date2001-09-25
dc.date2001-09-26
dc.date.accessioned2026-07-07T04:28:39Z
dc.date.available2026-07-07T04:28:39Z
dc.descriptionIn this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets, using newly devised techniques that may be applied to any linear equation (e.g., Schroedinger Equation in field theory, or the small-oscillations problem in mechanics). In particular, we improve a time-independent PB found recently which defines a Hamiltonian Structure for the HE, and we construct an Action Principle for the HE. We also find a new structure, which we call a Metric Structure, which may be used to define alternative anti-commutative "Hamiltonian" theories, in which the Metric- or M-Hamiltonians have to be explicitly time-dependent. Finally, we map some of these results to the Potential Burgers Equation.
dc.description15 pages, submitted to Journal of Physics A: Math. Gen. ; LaTeX2e, uses amsmath.sty and amssymb.sty
dc.identifierhttps://arxiv.org/abs/math-ph/0109026
dc.identifierhttp://arxiv.org/abs/math-ph/0109026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56869
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.titleLagrangian, Hamiltonian and other Structures for the Heat Equation and Potential Burgers Equation
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