A nonclassical algebraic solution of a 3-variable irregular Garnier system

Abstract

In this paper, a nonclassical algebraic solution of a 3-variable irregular Garnier system is constructed. Diarra-Loray have studied classification of algebraic solutions of irregular Garnier systems. There are two type of the algebraic solutions: classical type and pull-back type. They have shown that there are exactly three nonclassical algebraic solutions for N -variables irregular Garnier systems with N > 1. Explicit forms of two of the three solutions are already given. The solution constructed in the present paper is the remained algebraic solution.