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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.

##### MSC:
 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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