Abstract
Solitary waves in a spin chain with biquadratic anisotropic exchange interaction are investigated by means of the Holstein-Primakoff bosonic representation of spin operators. It is argued that the modified terms of the nonlinear Schrödinger equation are restricted strongly by the relative ratio of two small parameters η and ε used in long wave approximation and semiclassical approximation respectively. When assuming that η and ε2 have the same order (η−ε2, the so-called “super-long wave approximation”), after retaining terms of the equivalent order O(ε8), we find that the motion of Bose operator in the anisotropic case satisfies Schrödinger equation with high-order nonlinear term α|α|4. Its solitary wave solution and relevant physical results are discussed.
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