From a generalized discrete NLS equation in discrete alpha helical proteins to the fourth-order NLS equation. (December 2021) - Yang, Jun; Fang, Miao-Shuang; Luo, Lin; Ma, Li-Yuan
Highlights: We study a generalized integrable discrete nonlinear Schrodinger equation, which leads to the higher-order NLS equation in the continuum limit. The integrable properties of the generalized integrable discrete nonlinear NLS equation, including the discrete Lax pair, the Darboux Transformation and the soliton solutions, converge to their continuous counterparts as the discrete space step tends to zero. Darboux transformation and soliton solutions of the generalized discrete NLS equation are constructed. Abstract: In this paper, we consider a generalized integrable discrete nonlinear Schrödinger (NLS) equation, which can describe the dynamics of discrete alpha helical proteins with higher-order excitations and lead to the higher-order NLS equation in the continuum limit. The Darboux transformation (DT) and the soliton solutions of this generalized discrete NLS equation are implemented. It is shown that the integrable properties of the generalized discrete NLS equation, including the discrete Lax pair, the DT and the discrete soliton solutions, give rise to their continuous counterparts as the discrete space step tends to zero.