The existence of discrete solitons for the discrete coupled nonlinear Schrödinger system

Abstract

Abstract In this paper, we investigate the nonlinear coupled discrete Schrödinger equations with unbounded potentials. We find simple sufficient conditions for the existence of discrete soliton solution by using the Nehari manifold approach and the compact embedding theorem. Furthermore, by comparing the value of the action functional at the discrete soliton solution with those at nonzero solutions of one component zero, we demonstrate that both components of the discrete soliton solution are nontrivial.

Keywords

• Nonlinear Schrödinger lattice
• Discrete solitons
• Nehari manifold approach
• Compact embedding theorem