Bilinear forms and soliton solutions for a fourth-order variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain or an alpha helical protein

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• 作者：Jin-Wei Yang ; Yi-Tian Gao ; ^{gaoyt163@163.com" class="auth_mail" title="E-mail the corresponding author} ; Qi-Min Wang ; Chuan-Qi Su ; Yu-Jie Feng ; Xin Yu
• 关键词：87. 14. E ; 05. 45. Yv ; 47. 35. Fg
• 刊名：Physica B: Physics of Condensed Matter
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：481
• 期：Complete
• 页码：148-155
• 全文大小：6394 K

文摘

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.