On the discretization of Laine equations

Abstract

We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation which has that integral as an n-integral, or we proved that such an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable.

Keywords:

• Semi-discrete chain
• Darboux integrability
• x-integral
• n-integral
• discretization

2000 Mathematics Subject Classification:

• 35Q51
• 37K60