What physical mechanisms govern waves in non-conservative systems?

Jüri Engelbrecht
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Jüri Engelbrecht: Tallinn University of Technology Institute of Cybernetics, Centre for Nonlinear Studies (CENS)

Chapter Chapter 7 in Questions About Elastic Waves, 2015, pp 151-174 from Springer

Abstract: Abstract Most mathematical models described in the previous chapters are conservative like their prime example, the classical wave equation. Wave equation The celebrated KdV equation Korteweg-de Vries (KdV) equation is also conservative and admits infinitely many conserved quantities [2, 59]: 7.1 $$\displaystyle\begin{array}{rcl} \int _{-\infty }^{+\infty }u\mathit{dx} = \mathit{const}.,& &{}\end{array}$$ 7.2 $$\displaystyle\begin{array}{rcl} \int _{-\infty }^{+\infty }u^{2}\mathit{dx} = \mathit{const}.,& &{}\end{array}$$ 7.3 $$\displaystyle\begin{array}{rcl} \int _{-\infty }^{+\infty }(u^{3} + \frac{1} {2}u_{x}^{2})\mathit{dx} = \mathit{const}.,\ldots & &{}\end{array}$$ These equations express the conservation of mass Conservation of mass , momentum, and energy, respectively. The accuracy of a numerical method can be checked by calculating these conserved quantities at every time step.

Keywords: Solitary Wave; Mechanical Wave; Pseudospectral Method; Driving Field; Steady Wave (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-14791-8_7

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