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Nonlinear localized magnetic excitations in one dimensional magnonic crystalis investigated under periodic magntic field. The governing Landau-Lifshitzequation is transformed into variable coefficient nonlinear Schrodingerequation(VCNLS) using sterographic projection. The VCNLS equation is in generalnonintegrable, by using painleve analysis necessary conditions for the VCNLSequation to pass Weiss-Tabor-Carnevale (WTC) Painleve test are obtained. Asufficient integrability condition is obtained by further exploring atransformation, which can map the VCNLS equation into the well-known standardnonlinear Schrodinger equation. The transformation built a systematicconnection between the solution of the standard nonlinear Schrodinger equationand VC-NLS equation. The results shows the excitation of magnetization in theform of soliton has spatialperiod exists on the background of spin Bloch waves.Such solution exisits only certain constrain conditions on the coefficient ofthe VCNLS equation are satisfied. The analytical results suggest a way tocontrol the dynamics of magnetization in the form of solitons by an appropriatespatial modulation of the nonlinearity coefficient in the governing VCNLSequation which is determined by the ferromagnetic materials which forms themagnonic crystal.

Analytical soliton solution for the Landau-Lifshitz equation of one dimensional magnonic crystal