»ã±¨±êÌâ (Title)£ºReduction of lattice equations: Lecture I£¨ÀëÉ¢·½³ÌµÄÔ¼»¯£©

»ã±¨ÈË (Speaker)£º Peter van der Kamp ½ÌÊÚ£¨La Trobe University, Australia£©

»ã±¨¹¦·ò (Time)£º2022Äê09ÔÂ01ÈÕ(ÖÜËÄ) 09:00-10:00

»ã±¨µØÖ· (Place)£ºZoom»áÒé £¨ID£º882 4175 6007£©

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»ã±¨ÌáÒª£ºLecture 1 Topics: Lattice equations, Consistency Around the Cube, Lax pairs, including for multi-component systems

Narrative: A lattice equation is a relation between points on a lattice called a stencil, the stencil can be translated over the lattice and the corresponding equations should hold everywhere on the lattice. Often the stencil is an elementary square (of the 2D lattice), also called a quad. Such equations are called Consistent Around the Cube (CAC) if they can be consistently defined on the face of a 3D cube. CAC quad equations can be defined on more general quad-graphs and higher dimensional lattices. For a lattice equation which is CAC, one can derive a Lax pair, which is a system of linear equations whose consistency is equivalent to the equation. This procedure also works for systems of lattice equations.