Asymptotics at $t\to\infty$ of the solution of the Cauchy problem for the Landau–Lifshitz equation

Explicit expressions that describe the leading term in the asymptotic behavior of the solution of the Cauchy problem for the completely anisotropic Landau–Lifshitz equation in the solitonless sector are obtained. The employed method is based on direct asymptotic analysis of the corresponding matrix Riemann problem on a torus.