https://doi.org/10.1140/epjb/e2009-00356-3
Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation
1
School of Science, P. O. Box 122, Beijing University of
Posts and Telecommunications, 100876, Beijing, China
2
State Key Laboratory of Software Development Environment, Beijing
University of Aeronautics and Astronautics, 100191, Beijing, China
3
Key Laboratory of Information Photonics and Optical Communications (BUPT),
Ministry of Education, P.O. Box 128,
Beijing University of Posts and Telecommunications, 100876, Beijing, China
Corresponding author: a tian.bupt@yahoo.com.cn
Received:
24
February
2009
Revised:
29
June
2009
Published online:
22
October
2009
In this paper, analytically investigated is a higher-order dispersive nonlinear Schrödinger equation. Based on the linear eigenvalue problem associated with this equation, the integrability is identified by admitting an infinite number of conservation laws. By using the Darboux transformation method, the explicit multi-soliton solutions are generated in a recursive manner. The propagation characteristic of solitons and their interactions under the periodic plane wave background are discussed. Finally, the modulational instability of solutions is analyzed in the presence of small perturbation.
PACS: 05.45.Yv – Solitons / 02.30.Ik – Integrable systems / 02.30.Jr – Partial differential equations / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009
