In this article, we introduce the well-posedness of N.G-KdV class (3+1) equation which has an important physically phenomena of the propagation of traveling wave with all types solitary waves. We prove, first of all, that the general class of N.G-KdV class (3+1) equation can be reduced for certain data to a semi-linear system of first order partial differential equations. We find the characteristics of this system and show that it is equivalent to a system of ordinary differential equations in which differentiation is along characteristic direction. These equations can be integrated to give the solution of the system provided that the data is not specified on a characteristic. This method of solution is called the generalized characteristics in three dimensions.