## The duplication of frequency of laser radiation through nonlinear media |

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_ x _ 2r cos2Ba amp/meter Analogously assume Bassanini boundary conditions boundary value problem Cauchy problem characteristic lines computations constants continuous functions convergent cos(a)t cos(cJt cosB(y denote Department of Mathematics determine dimensionless duplication of frequency element equations 18 existence and uniqueness GAMMA(I GAO(I GAO(I,J GBO(I hence hyperbolic system hyperplane hypotheses I)av I)Cv identity matrix incoming wave integral equation iteration iterative scheme l+SA linear problem magnetic permeabilities Max Sup measured in meters method of successive nondimensional nonlinear problem numerical problem 21 problem 7,8 process of successive quartz crystal r'I)aNov region regressive wave relations ruby red laser satisfying Schauder's canonic form sec/meter SECOND HARMONIC speed of light successive approximations topology UJ UJ UJ UJ Ul unknowns E,H volt/meter ys+1 z_ot