A discrete negative AKNS equation: generalized Cauchy matrix approach

Abstract

Generalized Cauchy matrix approach is used to investigate a discrete negative Ablowitz–Kaup–Newell–Segur (AKNS) equation. Several kinds of solutions more than multi-soliton solutions to this equation are derived by solving determining equation set. Furthermore, applying an appropriate continuum limit we obtain a semidiscrete negative AKNS equation and after a second continuum limit we derive the nonlinear negative AKNS equation. The reductions to discrete, semi-discrete and continuous sine-Gordon equations are also discussed.

Keywords:

• discrete negative AKNS equation
• solution
• continuum limit
• reduction

2000 Mathematics Subject Classification:

• 39A14
• 35Q51
• 37K40