Perturbation Theory of Self-Oscillating System with a Periodic Perturbation

Self–Similar Perturbation Theory

A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather delicate questions: What can be said about the convergence of the calculational procedure when only a few its terms are available and how to decide which of ...

Rayleighachrodinger perturbation theory with a strong perturbation: anharmonic oscillators

The bound state solutions of Schrodinger’s equation for the anharmonic oscillator potentials V = x2+ AxZk ( k = 2 , 3 , . . .) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator ( k = 2) a scaled harmonic potential provides a remarkably accurate model for all A. Although this model is slightly less satisfactory for higher...

Perturbation Theory with Instantons

The large k asymptotics (perturbation series) for integrals of the form ∫ F μe ikS , where μ is a smooth top form and S is a smooth function on a manifold F , both of which are invariant under the action of a symmetry group G, may be computed using the stationary phase approximation. This perturbation series can be expressed as the integral of a top form on the space M of critical points of S m...

A modified homotopy perturbation method to periodic solution of a coupled integrable dispersionless equation

In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and...

Perturbation of Periodic Boundary-Conditions