ON A NUMERICAL METHOD OF A NON-LINEAR BOUNDARY PROBLEM SOLUTION WITH EIGENVALUES FOR ELECTROMAGNETIC TM-WAVES DISTRIBUTED IN THE LAYER WITH KERR’S NON-LINEARITY

Zarembo Ekaterina Viktorovna, Applicant, sub-department of mathematics and supercomputer modeling, Penza State University, mmm@pnzgu.ru

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The article considers electromagnetic TM-waves propagation in a layer with Kerr nonlinearity. The physical problem is reduced to a nonlinear boundary Eigenvalue problem for a system of two ordinary differential equations. A new method for solving the nonlinear boundary eigenvalue problem is suggested. The method can be applied to study more complicated nonlinearities. Some numerical results are shown.

nonlinear boundary eigenvalue problem, ordinary differential equation, Cauchy problem.