Dark soliton collisions for a fourth-order variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain or alpha helical protein

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• 作者：Xi-Yang Xie ; Bo Tian ; Jun Chai ; Xiao-Yu Wu ; Yan Jiang
• 关键词：Heisenberg ferromagnetic spin chain ; Alpha helical protein chain ; Fourth ; order variable ; coefficient nonlinear Schrödinger equation ; Hirota method ; Dark soliton collisions
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：86
• 期：1
• 页码：131-135
• 全文大小：1,691 KB
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：86

文摘

Under investigation in this paper is a fourth-order variable-coefficient nonlinear Schrödinger equation, which can describe an inhomogeneous one-dimensional anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein. With the aid of the Hirota method and symbolic computation, bilinear forms, dark one- and two-soliton solutions are obtained. Influences of the variable coefficients on the dark one and two solitons are graphically shown and discussed. Amplitude and shape of the dark one soliton keep invariant during the propagation when the variable coefficients are chosen as the constants. With the variable coefficients being the functions, amplitude of the dark soliton keeps unchanged during the propagation, but direction of the soliton curves. Head-on and overtaking collisions between the dark two solitons are displayed with the variable coefficients chosen as the constants, and it is shown that the shapes of the two solitons do not change during the collision. When we choose the variable coefficients as the functions, directions of the two solitons change and elastic collisions occur between the two solitons.