Stochastic quantization of laser propagation models

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling Laser propagation through turbulent media. In some typical physical contexts, problem reduces to Schrödinger equation with space–time white noise Gaussian or Poisson Lévy type. We identify their resolution via quantization. Nonlinear phenomena such as Kerr effect can be modeled by a nonlinear focusing case noise. A treatment transport equation, Korteweg–De Vries well number other wave equations is also given. The main technique S-transform (we will actually use closely related Hermite transform) which converts partial differential (PDE) deterministic PDE defined on Hida–Kondratiev distribution space. then utilize inverse S-transform/Hermite transform known characterization theorem combined infinite-dimensional implicit function for analytic maps establish local existence and uniqueness theorems path-wise solutions this class problems. particular focus singular distributions motivated practical situations where refractive index fluctuations medium space time are intense due turbulence, ionospheric plasma marine-layer fluctuations, etc. Since large PDEs, that arise propagation, have polynomial-type nonlinearities, theory an effective tool studying these subject different types noises.