Journal
PHYSICS LETTERS A
Volume 384, Issue 2, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2019.126064
Keywords
Nonlinear wave propagation; Hodograph transformation; Lagrangian-Hamiltonian formalism
Categories
Funding
- European Regional Development Fund [CZ.02.1.01 0.0/0.0/15_003/0000449]
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The hodograph transformation is generally used in order to associate a system of linear partial differential equations to a system of nonlinear (quasilinear) differential equations by interchanging dependent and independent variables. Here we consider the case when the nonlinear differential system can be derived from a Lagrangian density and revisit the hodograph transformation within the formalism of the Lagrangian-Hamiltonian continuous dynamical systems. Restricting to the case of nondissipative, nondispersive one-dimensional waves, we show that the hodograph transformation leads to a linear partial differential equation for an unknown function that plays the role of the Lagrangian in the hodograph variables. We then define the corresponding hodograph Hamiltonian and show that it turns out to coincide with the wave amplitude. i.e., with the unknown function of the independent variables to be solved for in the initial nonlinear wave equation. (C) 2019 Elsevier B.V. All rights reserved.
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