Bilinear forms, N-soliton solutions and soliton interactions for a fourth-order dispersive nonlinear Schr?dinger equation in condensed-matter physics and biophysics

摘要

In this paper we investigate a fourth-order dispersive nonlinear Schr?dinger equation, which governs the dynamics of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain with the octuple-dipole interaction in condensed-matter physics as well as the alpha helical proteins with higher-order excitations and interactions in biophysics. Beyond the existing constraint, upon the introduction of an auxiliary function, bilinear forms and N-soliton solutions are constructed with the Hirota method. Asymptotic analysis on the two-soliton solutions indicates that the soliton interactions are elastic. Soliton velocity varies linearly with the coefficient of discreteness and higher-order magnetic interactions. Bound-state solitons can also exist under certain conditions. Period of a bound-state soliton is inversely correlated to the coefficient of discreteness and higher-order magnetic interactions. Interactions among the three solitons are all pairwise elastic.