
13.3. BRIGHT INCOHERENT SOLITONS
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This equation represents a continuity equation, implying the conservation of the num-
ber of quasi-particles in the phase space. Using the Liouville theorem, we can obtain
the canonical Hamilton equations of motion for a quasi-particle of mass d or, equiva-
lently, the ray equations of the geometrical-optics approximation, with r and p playing
the role of the canonical variables. Equation (13.2.27) is similar to the radiative transfer
equation used in Refs. [48] and [49].
The Wigner transform method provides an equivalent way to treat the propaga-
tion of partially coherent fields in nonlinear ...