Computational Mathematics and Mathematical Physics

, Volume 58, Issue 11, pp 1856–1864 | Cite as

Soliton Solutions and Conservation Laws for an Inhomogeneous Fourth-Order Nonlinear Schrödinger Equation

  • Pan Wang
  • Feng-Hua Qi
  • Jian-Rong Yang


In this paper, we investigate an inhomogeneous fourth-order nonlinear Schrödinger (NLS) equation, generated by deforming the inhomogeneous Heisenberg ferromagnetic spin system through the space curve formalism and using the prolongation structure theory. Via the introduction of the auxiliary function, the bilinear form, one-soliton and two-soliton solutions for the inhomogeneous fourth-order NLS equation are obtained. Infinitely many conservation laws for the inhomogeneous fourth-order NLS equation are derived on the basis of the Ablowitz–Kaup–Newell–Segur system. Propagation and interactions of solitons are investigated analytically and graphically. The effect of the parameters \({{\mu }_{1}}\), \({{\mu }_{2}}\), \({{\nu }_{1}}\) and \({{\nu }_{2}}\) on the soliton velocity are presented. Through the asymptotic analysis, we have proved that the interaction of two solitons is not elastic.


inhomogeneous generalized fourth-order nonlinear Schrödinger equation infinitely many conversation laws auxiliary function Hirota method symbolic computation 



We express our sincere thanks to the teachers and students for their helpful suggestions. This work has been supported by the National Natural Science Foundation of China under Grant nos. 11426041 and 11605011, and the Fundamental Research Funds for the Central Universities.


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.School of Management, Beijing Sport University, Information Road Haidian DistrictBeijingChina
  2. 2.School of Information, Beijing Wuzi UniversityBeijingChina

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