Kuznetsov-Ma solution and Akhmediev breather for TD equation

Abstract

We present the inverse scattering transform for the TD equation, which is related to the Heisenberg spin equation. We note that the TD equation is an integrable model with high nonlinearity, and has singularity at zero. Thus a nonzero boundary condition is introduced in the direct scattering problem. We obtain the $N$-solitonic solution of the TD equation, and give the Kuznetsov-Ma type solution, rational solution and Akhmediev type breather.