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Extended Generalized Hyperbolic-function Method and New Exact Solutions of the Generalized Hamiltonian and NNV Equations by the Symbolic Computation

Liu J.-G., Zeng Z.-F.

Fundamenta Informaticae

2014

Vol. 132, nr 4

501--517

In this paper, with the aid of the computerized symbolic computation, we present an extended generalized hyperbolic-function method. Being concise and straightforward, it can be applicable to seek more types of solutions for certain nonlinear evolution equations (NLEES). In illustration, we choose the generalized Hamiltonian equations and the (2 + 1)-dimensional Nizhnik- Novikov-Veselov (NNV) equations to demonstrate the validity and advantages of the method. As a result, abundant new exact solutions are obtained including soliton-like solutions, traveling wave solutions etc. Themethod can be also applied to other nonlinear partial differential equations (NPDEs).

The unsteady Couette flow of a second grade fluid n a layer of porous medium

Hayat T., Khan M., Ayub M., Siddiqui A. M.

Archives of Mechanics

2005

Vol. 57, nr 5

405--416

In this work, the two Couette flows of a second grade fluid are discussed in a porous layer when (i) bottom plate moves suddenly (ii) bottom plate oscillates. Laplace transform method is used to determine the analytic solutions. Expressions for the velocities, volume fluxes and frictional forces are constructed.