Open AccessTHE HIERARCHY OF ASSOCIATIVITY EQUATIONS FOR n=3 CASE WITH AN METRIC ƞ11≠0
Author(s) -
A.A. Жадыранова,
Ж.Р. Мырзакул,
Kairat Myrzakulov
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-1.1728-7901.34
Subject(s) - associative property , mathematics , nonlinear system , hierarchy , integrable system , metric (unit) , topological quantum field theory , covariant transformation , field (mathematics) , pure mathematics , quantum field theory , partial differential equation , mathematical physics , topology (electrical circuits) , mathematical analysis , physics , quantum mechanics , operations management , combinatorics , economics , market economy
This paper describes the hierarchy for N = 2 and n=3 case with an metric ƞ11≠0 when V0 = 0 of associativity equations. The equation of associativity arose from the 2D topological field theory. 2D topological field theory represent the matter sector of topological string theory. These theories covariant before coupling to gravity due to the presence of a nilpotent symmetry and are therefore often referred to as cohomological field theories. We give a description of nonlinear partial differential equations of associativity in 2D topological field theories as integrable nondiagonalizable weakly nonlinear homogeneous system of hydrodynamic type. The article discusses nonlinear equations of the third order for a function f = f(x,t)) of two independent variables x, t. In this work we consider the associativity equation for n=3 case with an a metric 0 11 . The solution of some cases of hierarchy when N = 2 and V0 = 0 equations of associativity illustrated