Analytical solutions are obtained to the nonlinear equations describing neutrino oscillations when explicit neutrino-antineutrino asymmetries are present. Such a system occurs in the early Universe if neutrinos have a non-zero chemical potential. Solutions to the equations lead to a new type of coherent behavior governed by two modes. These bimodal solutions provide new insights into dense neut...

Aims. We present the basic equations and sample solutions for the steady-state global transonic solutions of the advection-dominated accretion flows (ADAFs) with causal viscosity prescription. The procedures of the stable numerical calculations and all explicit formula to obtain the solutions of ADAFs are also presented. Methods. We solve the transonic solutions of ADAFs by using the explicit n...

We apply an analytical method called the Optimal Parametric Iteration Method OPIM to multispecies Lotka-Volterra equations. By using initial values, accurate explicit analytic solutions have been derived. The method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement has been demons...

An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative, and combinatorial-recursive calculations of multidimensional integral expressions, which can describe partial solutions of these problems, are presented (the...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.