Darboux transformation and conservation laws for an inhomogeneous fifth-order nonlinear Schrödinger equation from the Heisenberg ferromagnetism

2015 ◽  
Vol 20 (3) ◽  
pp. 692-698 ◽  
Author(s):  
Ming Wang ◽  
Wen-Rui Shan ◽  
Bo Tian ◽  
Zhao Tan
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Fifth Order

N-fold Darboux transformation, conservation laws and modulation instability for the semi-discrete coupled nonlinear Schrödinger equation

2017 ◽  
Vol 31 (16) ◽  
pp. 1750174 ◽  
Author(s):  
Xiao-Juan Zhao ◽  
Hui-Qin Hao
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Nonlinear Schrodinger Equation ◽  
Dynamic Features ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation

In this paper, a semi-discrete coupled nonlinear Schrödinger equation is investigated via the Darboux transformation (DT) method. Based on the Lax pair, the N-fold DT and conservation laws are constructed. Some new discrete soliton solutions under the vanishing and nonvanishing backgrounds are also derived. The dynamic features of those solutions are displayed through figures. The modulation instability (MI) is analyzed and the dispersion relation is derived.

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