Hierarchy of WDVV associativity equations for n = 3 case and N = 2 when V06= 0
We investigate solutions of Witten-Dijkgraaf-E.Verlinde-H.Verlinde (WDVV) equa-tions. The article discusses nonlinear equations of the third order for a function f = f(x, t) ) oftwo independent variables x, t . The solution of some cases of hierarchy equations of associativityillustrated. Lax pairs for the system of three equations, that contains the equation of associativityare written to ﬁnd the hierarchy of associativity equation. Using the compatibility condition arefound the relations between the matrices U, V2, V1, V0. The elements of matrix V2are found withthe expression of zijand independent and dependent variables for the matrix V2. Also solvingelements of matrix V1expressed through yijand independent and dependent variables for thematrix V1. The elements of matrix V0are found with the expression of rijand independent anddependent variables for the matrix V0too. Expressed are variables at, bt, ctof three equationsare written with the help of matrix elements zij, yij.