METHOD OF GENERALIZED JACOBI ELLIPTIC FUNCTIONS FOR SOLVING SOME CLASSES OF NONLINEAR ELLIPTIC SYSTEMS OF SECOND-ORDER EQUATIONS ON THE PLANE

 Inthis paper, generalized Jacobi elliptic functions snω(z), cnω(z), dnω(z) are applied to the construction of particular solutions of certain classes of elliptic systems of partial differential equations of second order on the complex plane C with Cauchy–Riemann operators 2∂z = ∂x + i∂y, 2∂z = ∂x − i∂y, the Laplace operator ∆ = 4∂z(∂z) = ∂xx + ∂yy, and the Bitsadze operator
4∂2 zz = 4∂z(∂z) = ∂xx−∂yy+2i∂2 xy, where the variables z = x+iy, z = x−iy are independent.