Breathers on elliptic function background for a generalized nonlinear Schrodinger equation with higher-order terms

A generalized nonlinear Schrodinger equation with higher-order terms, which is derived as a model for the nonlinear spin excitations in the one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin, is investigated. Firstly, in view of Riccati equations associated with the Lax pair, the Darboux transformation of a generalized nonlinear Schrodinger equation is presented. Secondly, the complicated Jacobi elliptic functions as seed solutions are considered so that much more fascinating solutions and dynamical properties can be obtained. Based on the above discussion, breathers in the presence of two kinds of Jacobian elliptic functions dn and cn are constructed. Finally, the dynamical properties of such solutions are analyzed by drawing the three-dimensional figures. The structures of these solutions are influenced by the higher-order operator. More importantly, the method provided in this paper can also be adopted to construct breathers on the elliptic functions background of other higher-order nonlinear integrable equations.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

In this study, a generalized nonlinear Schrodinger equation with higher-order terms is investigated as a model for the nonlinear spin excitations in the one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin. The Darboux transformation of the equation is presented using Riccati equations associated with the Lax pair. By considering complicated Jacobi elliptic functions as seed solutions, breathers in the presence of two kinds of Jacobian elliptic functions are constructed. The dynamical properties of these solutions are analyzed using three-dimensional figures.