Nonlinear evolution of wave packets in magnetic fluids

Malik, S. K.; Singh, M.

doi:10.1090/qam/1074957

Authors: S. K. Malik and M. Singh
Journal: Quart. Appl. Math. 48 (1990), 415-431
MSC: Primary 76W05
DOI: https://doi.org/10.1090/qam/1074957
MathSciNet review: MR1074957
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Abstract: The propagation of wave packets on the surface of a magnetic fluid of finite depth is considered in $\left ( {2 + 1} \right )$ dimensions. It is shown that the evolution of the envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of more than one region of instability. The enveloping soliton and the “waveguide” solutions are derived in the regions of instability wherever they exist in one space dimension. The instability regions are sensitive to the applied magnetic field strength. The evolution of the envelope is governed by a $\left ( {2 + 1} \right )$-dimensional nonlinear equation which leads to a self-focussing singularity. Examined also is the long wave/short wave resonant interaction in magnetic fluids. Our study shows that the application of the magnetic field decreases the region of instability where this resonance occurs.

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