Many applications of various self-adjoint differential equations, whose solutions are complex, are produced Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011 . In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefi...

In this paper, variational iteration method (VIM) is applied to obtain approximate analytical solution of the (2 + 1)-dimensional potential Kadomtsev-Petviashvili equation (PKP) without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

The ground state and the excitation spectrum of strongly correlated electrons in quantum dots are investigated. An analytical solution is constructed by exact diagonalization of the Hamiltonian in terms of the N-particle eigenmodes.

The benefit of finding particular exact and asymptotic solutions of non-integrable non-linear partial differential equations is considered. It is shown how explicit analytical solutions predict important features of the waves behavior even outside their formal applicability. In particular, an arbitrary initial pulse splits in a numerical solution into the train of localized waves each described...

We obtain the exact analytical solution for continuously driven qutrit in V and $\Lambda$ configurations governed by Lindblad master equation. calculate linear susceptibility each system, determining regimes of transient gain without inversion, identify parameter values superluminal, vanishing, negative group velocity probe field.