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Variational principle for nonlinear wave propagation in dissipative systems

Hans Dierckx (UGent) and Henri Verschelde (UGent)
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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.
Keywords
SCROLL WAVES, EXCITABLE MEDIA, SPIRAL WAVES, EQUATIONS, FILAMENTS, DYNAMICS

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Please use this url to cite or link to this publication:

Chicago
Dierckx, Hans, and Henri Verschelde. 2016. “Variational Principle for Nonlinear Wave Propagation in Dissipative Systems.” Physical Review E 93 (2).
APA
Dierckx, H., & Verschelde, H. (2016). Variational principle for nonlinear wave propagation in dissipative systems. PHYSICAL REVIEW E, 93(2).
Vancouver
1.
Dierckx H, Verschelde H. Variational principle for nonlinear wave propagation in dissipative systems. PHYSICAL REVIEW E. 2016;93(2).
MLA
Dierckx, Hans, and Henri Verschelde. “Variational Principle for Nonlinear Wave Propagation in Dissipative Systems.” PHYSICAL REVIEW E 93.2 (2016): n. pag. Print.
@article{8152606,
  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.},
  articleno    = {022210},
  author       = {Dierckx, Hans and Verschelde, Henri},
  issn         = {2470-0045},
  journal      = {PHYSICAL REVIEW E},
  keywords     = {SCROLL WAVES,EXCITABLE MEDIA,SPIRAL WAVES,EQUATIONS,FILAMENTS,DYNAMICS},
  language     = {eng},
  number       = {2},
  pages        = {6},
  title        = {Variational principle for nonlinear wave propagation in dissipative systems},
  url          = {http://dx.doi.org/10.1103/PhysRevE.93.022210},
  volume       = {93},
  year         = {2016},
}

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