Mathematics & Physics 2017, 10(1), 55–59 УДК 537.61 Continual Approach in the Mean Field Theory of Incommensurate Magnetic States in the Frustrated Heisenberg Ferromagnet Sergey N.Martynov Vasiliy I.Tugarinov∗ Kirensky Institute of Physics, SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036 Russia Aleksandr S.Martynov Faculty of Physics Moscow State University Moscow, 119991 Russia Received 20.08.2016, received in revised form 10.10.2016, accepted 15.11.2016 The algorithm of approximate solution has been developed for the differential equation describing the anharmonical change of the spin orientation angle in the model of ferromagnet with the exchange competition between nearest and next nearest magnetic neighbors and the easy axis exchange anisotropy. <...> The obvious dependence of the angle velocity from angle and initial condition has been derived by expanding the first integral of the equation in the Taylor series in vicinity of initial condition. <...> The theoretical description of incommensurate magnetic structures (IMS) in antiferromagnetic dielectrics in the framework of Landau phenomenological theory of the phase transition was elaborated by Dzyaloshinskii [1]. <...> For helimagnet with the Dzialoshinskii-Moria antisymmetrical exchange leading to a Lifshitz invariant in a free energy expansion (relativistic mechanism of forming IMS) the energy minimization for the solutions within the anisotropic plane is reduced to the solution of static sine-Gordon equation. <...> The equation has the anharmonic solutions in the form of elliptical integrals describing the inhomogeneous helical structure with the step changing when moving along the helix vector - the so called soliton lattice [2]. <...> For helimagnets with competing exchange interactions between the nearest and further magnetic neighbours (the exchange mechanism) it is necessary to take into consideration the second derivatives (and highter ones in the general case) of an order parameter and the energy minimization can not be reduced to an analiticaly integrable differential equation. <...> The aim of the present work is to develop the algorithm of approximate solution for the equation describing the anharmonic change of the spin orientation angle in the easy axis ferromagnet with the exchange competition between the nearest and next nearest neighbors. <...> We consider the magnetic structure with the spin orientation within the anisotropy plane (the flat anharmonic helix) and depends on the one coordinate. ∗unonav@iph.krasn.ru ⃝ Siberian Federal University. <...> All rights reserved c – 55 – S.N. Martynov, V.I.Tugarinov, A.S.Martynov Continual <...>