HIERARCY OF WDVV ASSOCIATIVITY EQUATIONS FOR n = 3 AND N = 2 CASE WHEN = 0 V0 WITH NEW SYSTEM t t t - A.A. Zhadyranova (Academic Scientific Journal of Computer Science, 2019)
We investigate solutions of Witten-Dijkgraaf-E.Verlinde-H.Verlinde (WDVV) equations. The article discusses nonlinear equations of the third order for a function f = f(x,t)) of two independent variables x,t. The equations of associativity reduce to the nonlinear equations of the third order for a function f = f(x,t)) when prepotential F dependet of the metric η. In this work we consider the WDVV equation for n = 3 case with an antidiagonal metric η. The solution of some cases of hierarchy equations of associativity illustrated. Lax pairs for the system of three equations, that contains the equation of associativity are written to find the hierarchy of associativity equation. Using the compatibility condition are found the relations between the matrices U, V2, V1. The elements of matrix V2 are found with the expression of zij and independent and dependent variables for the matrix V2. Also solving elements of matrix V1 expressed through yij and independent and dependent variables for the matrix V1. We accepted that elements of matrix V0 are zero. In the physical setting the solutions of WDVV describe moduli space of topological conformal field theories [1, 2]. Let us introduce new variables a, b, c. In the above variables the nonlinear equations of the third order for a function f = f(x,t)) we rewritten as a new system of three equations. Expressed are variables at ,bt ,ct of three equations are written with the help of matrix elements zij ,yij.