Asymptotic behavior as $t\to\infty$ of the solution to the Cauchy problem for the Landau–Lifshitz equation

The leading term in the $t\to\infty$ asymptotic behavior of the solution of the Cauchy problem for the Landau–Lifshitz equation is constructed in the case of “rapidly decreasing” initial data. The interaction of the oscillator background due to the continuum with soliton excitations is described.