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Dierckx H, Verschelde H. Variational principle for nonlinear wave propagation in dissipative systems. Phys Rev E. 2016;93(2):022210doi: 10.1103/PhysRevE.93.022210.
Dierckx, H., & Verschelde, H. (2016). Variational principle for nonlinear wave propagation in dissipative systems. Physical review. E, 93(2), 022210. https://doi.org/10.1103/PhysRevE.93.022210
Dierckx, Hans, and Verschelde, Henri. "Variational principle for nonlinear wave propagation in dissipative systems." Physical review. E vol. 93,2 (2016): 022210. doi: https://doi.org/10.1103/PhysRevE.93.022210
Dierckx H, Verschelde H. Variational principle for nonlinear wave propagation in dissipative systems. Phys Rev E. 2016 Feb;93(2):022210. doi: 10.1103/PhysRevE.93.022210. Epub 2016 Feb 16. PMID: 26986334.
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Phys Rev E. 2016 Feb;93(2):022210. doi: 10.1103/PhysRevE.93.022210. Epub 2016 Feb 16.

Variational principle for nonlinear wave propagation in dissipative systems.

Physical review. E

Hans Dierckx, Henri Verschelde

Affiliations

  1. Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium.

PMID: 26986334 DOI: 10.1103/PhysRevE.93.022210

Abstract

The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.

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