New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

in this study, a generalized equation is presented to calculate vapor pressure of pure substances as a function of reduced temperature, critical pressure, and acentric factor. with the presented model, vapor pressures have been calculated and evaluated with nist data bank for 70 pure substances for about 14000 data points, and the overall average absolute percentage deviation has been only 0.78...

It is well known that the Schrödinger equation is only suitable for the particle in common potential V (~r, t). In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave equation can describe the particle which is in general potential V (~r, ~̇r, t). We think these new quantum wave equations can be applied in many fields. PACS numbers:...