Time reversal symmetry: Difference between revisions

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* For [[KdV-type equations]], the time reversal of a solution <math>u(t,x)</math> is usually <math>u(-t,-x)</math>.
* For [[KdV-type equations]], the time reversal of a solution <math>u(t,x)</math> is usually <math>u(-t,-x)</math>.


[[Category:Transform]]
[[Category:Transforms]]

Revision as of 01:26, 15 August 2006

Time reversal symmetry refersto any symmetry in which every solution to a dispersive equation comes with a counterpart which evolves backwards in time compared to the original solution, thus the original solution at time t is linked to the reversed solution at time -t. While most dispersive model equations enjoy a time reversal symmetry, this symmetry manifests itself differently from equation to equation:

  • For wave equations, the time-reversal of a solution is usually , although for tensor-valued fields one may also have to negate certain "time components" of the field.
  • For Schrodinger equations, the time-reversal of a solution is usually .
  • For KdV-type equations, the time reversal of a solution is usually .