Non-homogeneous Hamiltonian structures for quasilinear systems
Pierandrea Vergallo
TL;DR
This paper explores conditions under which certain first-order PDE systems are Hamiltonian, extending compatibility conditions to degenerate operators and providing illustrative examples.
Contribution
It introduces necessary and sufficient conditions for non-homogeneous Hamiltonian structures in quasilinear PDEs, extending Tsarev's compatibility conditions to degenerate cases.
Findings
Extended Tsarev's compatibility conditions to degenerate operators
Identified criteria for Hamiltonian structures with non-homogeneous operators
Discussed examples illustrating the theoretical results
Abstract
This paper aims at investigating necessary (and sufficient) conditions for quasilinear systems of first order PDEs to be Hamiltonian, with non-homogeneous operators of order 1 + 0, also with degenerate leading coefficient. As a byproduct, Tsarev's compatibility conditions are extended to degenerate operators. Some examples are finally discussed.
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Taxonomy
TopicsNumerical methods for differential equations · Nonlinear Waves and Solitons · Differential Equations and Numerical Methods