HIERARCY OF WDVV ASSOCIATIVITY EQUATIONS FOR n = 3 AND N = 2 CASE WHEN = 0 0 V WITH NEW SYSTEM t t t
Ключевые слова:
equations of Witten-Dijkgraaf-E.Verlinde-H.Verlinde, the equations of associativity, nonlinear equations of the third order, antidiagonal metric, the Lax pair, the compatibility condition, independent elements, dependent variables, system with equations.Аннотация
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.
