Breathers on elliptic function background for a generalized nonlinear Schrödinger equation with higher-order terms. (English) Zbl 1540.35376
Summary: A generalized nonlinear Schrödinger 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 Schrödinger 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 \(d n\) and \(c n\) 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.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
generalized nonlinear Schrödinger equation; Darboux transformation; elliptic function background; breathersReferences:
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