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

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 functio...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2018-11, Vol.58 (11), p.1856-1864
Main Authors: Wang, Pan, Qi, Feng-Hua, Yang, Jian-Rong
Format: Article
Language:English
Subjects:
Computational mathematics
Computational Mathematics and Numerical Analysis
Conservation laws
Deformation
Ferromagnetism
Investigations
Mathematical analysis
Mathematics
Mathematics and Statistics
Physics
Prolongation
Propagation
Schrodinger equation
Solitary waves
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Summary: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 , , and on the soliton velocity are presented. Through the asymptotic analysis, we have proved that the interaction of two solitons is not elastic.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542518110106