Solutions for a System of Difference-Differential Equations Related to the Self-Dual Network Equation

K. Narita
2001 Progress of theoretical physics  
We propose a system of difference-differential equations related to the self-dual network equation. By utilizing a Bäcklund transformation equation for the Toda lattice, we derive its N -soliton solution under nonvanishing boundary conditions at infinity. We present explicit expressions of four types of its 1-soliton solutions and examine them. Next, we present new formulas for finding rational solutions, and using them, we determine and analyze four types of rational solutions for these
more » ... ns for these equations. Finally, we derive their elliptic function solution.
doi:10.1143/ptp.106.1079 fatcat:fqkwh5737zczfir4dc6ktozz5a