This work presents the model equations governing the excitation of weak whistler by a stronger Kinetic Alfvén wave (KAW) in the plasma having β value (β ≫ me/mi, where beta is the ratio of the ion sound speed to the Alfvén speed), applicable to magnetotail in Earth's magnetosphere, when the ponderomotive nonlinearity is incorporated in the KAW dynamics. Numerical solution of the model equations has been obtained when the incident pump KAW is having a small perturbation. Energy exchange between main KAW and perturbation and the resulting localized structures of the KAW have been studied. A weak whistler signal propagating in these localized structures is amplified and leads to the development of envelope solitons. Our result reveals that the amplified (excited) whistler has an electric field power spectrum that is steeper than k-8/3. This result is consistent with recent observations by the Cluster spacecraft Eastwood et al. (Phys. Rev. Lett., vol. 102, 2009, 035001) in the magnetotail region of the Earth's magnetosphere.