The Lie method is used to derive the symmetry group of various sets of wave equations, and Noether's theorem is applied to find conservation laws of the wave equations. Symmetries and conservation laws of the wave equations of scalar statistical optics and vector statistical optics are studied and compared to the symmetries and conservation laws of the wave equations of deterministic wave optics. Generalizations of the deterministic conservation laws are found and seen to correspond to the usual laws in the deterministic limit. In the scalar statistical optics case, symmetries of two-time and stationary wave equations are compared. The statistically stationary wave equations are shown not to contain inversion symmetries, so the conservation laws differ from the conservation laws of the two-time wave equations. In the vector statistical optics case, continuous Larmor-Rainich-like symmetries are found among the dependent variables. Nongeometrical symmetries of these sets of equations, which are infinitesimal but not continuous, are also studied.
|Advisor:||Carney, P. Scott|
|School:||University of Illinois at Urbana-Champaign|
|School Location:||United States -- Illinois|
|Source:||DAI-B 69/11, Dissertation Abstracts International|
|Keywords:||Lie groups, Statistical optics, Wave equations|
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