Isomonodromic problem for analogue of the Painlevé equations

[摘要] A fourth-order analogue for the Painlevé equations that is self-similar reduction of the modified Sawada-Kotera and Kaup-Kupershmidt equation is considered. Zero curvature representation of Lax pair for the modified Sawada-Kotera equation is presented. Linear problem for a fourth-order analogue for the Painlevé equations is obtained from Lax pair for the modified Sawada-Kotera equation using self-similar variables.

[发布机构] National Research Nuclear University MEPhl, Kashirskoe sh. 31, Moscow; 115409, Russia^1

[效力级别] 数学

[关键词] Curvature representation;Fourth order;Lax pairs;Linear problems;Self-similar