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Fourth-order evolution equations for a surface gravity wave packet in a two layer fluid

100%

Senapati S. , Debsarma S. , Das K. P.

International Journal of Applied Mechanics and Engineering

2010

tom Vol. 15, no 4

1215-1225

Fourth order nonlinear evolution equations are derived for a three dimensional surface gravity wave packet in the presence of long wave length an interfacial wave in a two layer fluid domain in which the lower fluid depth is infinite. For derivation of evolution equations, the multiple-scale method is used. Using these evolution equations, stability of uniform stokes wavetrain is investigated for different values of density ratio of the two fluids and for different values of the depth of the lighter fluid.

Group invariant solution of some time fractional evolution equations

67%

Mandal H. , Bira B.

Journal of Applied Mathematics and Computational Mechanics

2018

tom Vol. 17, nr 4

35--46

In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.