Power Series Solutions of Higher Order Differential Equations for the Hypersensitive Congenial BIS Processes and Shock Waves in the Neuronal Nanosystem

BIS signifies the breakdown of integrated system. In order to discuss the perturbation in the neuronal system of it is necessary to superimpose a small BIS disturbance on these solutions and analyze the evolution of the small disturbance. This is equivalent to those solutions of nonlinear evolution equations which are expanded as a power series in terms of a small parameter ε. In this paper, on the basis of the Jacobi elliptic function expansion method, the multi-order exact solutions of some nonlinear evolution equations for the congenial and hypersensitive BIS processes are obtained. In this paper, based on Jacobi elliptic function expansion method, the Lame equation, and the Lame functions, the stationary periodic solutions to some non linear evolution equations for the neuronal nano systems and shock waves have been derived. At the same time the perturbation method is applied to obtain their asymptotic power series solutions. We have tried our best here to find out all the possible solutions of the equations evolved due to perturbation in the neuronal networks giving forth the chaos in the mind.