Exact Solutions for the Free Vibration in an Asymmetrical Duffing Equation.

Existence of Periodic Solutions for the Duffing Equation with Impulses

Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.

Exact Multiplicity for Periodic Solutions of Duffing type

In this paper, we study the following Duffing-type equation: x′′ + cx′ + g(t, x) = h(t), where g(t, x) is a 2π-periodic continuous function in t and concave-convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

2 3 M ay 2 00 7 Dirac equation exact solutions for generalized asymmetrical Hartmann potentials

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of generalized vector and scalar Hartmann potentials. This is done provided the vector and scalar potentials hold some relation. Namely, one must be equals to or minus the other. Finally the case of some quasi-exactly solvable potentials are briefly commented.

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow