Time reversal symmetry

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 $u(t,x)$ is usually $u(-t,x)$, 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 $u(t,x)$ is usually ${\overline {u}}(-t,x)$.

• For KdV-type equations, the time reversal of a solution $u(t,x)$ is usually $u(-t,-x)$.