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Solitary wave, breather wave and rogue wave solutions of an inhomogeneous fifth-order nonlinear Schrödinger equation from Heisenberg ferromagnetism. (English) Zbl 1412.35306
Summary: In this paper, we consider an inhomogeneous fifth-order nonlinear Schrodinger equation from Heisenberg ferromagnetism, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Based on its Lax pair, we study the determinant representation of the \(n\)-fold Darboux transformation (DT). Furthermore, by using the \(n\)-fold DT, we obtain the higher-order solitary wave, breather wave and rogue wave solutions of the equation, respectively. Finally, the dynamic characteristics of these exact solutions are discussed.

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q15 Riemann-Hilbert problems in context of PDEs
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
35Q41 Time-dependent Schrödinger equations and Dirac equations
82D40 Statistical mechanical studies of magnetic materials
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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