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This paper focuses on the compound phenomenon of Instability and Imbibition called Fingero-Imbibition phenomenon arising in two immiscible phase (oil and water) flow through homogeneous porous media in vertical downward direction. Mathematical formulation leads to non linear partial differential equation. The analytical solution is obtained by using generalised separable method in terms of quadratic polynomial by using appropriate boundary conditions and its physical interpretation is given with numerical tabulated values and graphical presentation.

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This paper presents Variational Homotopy Perturbation method for the nonlinear GeneralizedRegularized Long Wave (GRLW) equation. The solution of nonlinear GRLW equation is obtained and is solved using the iteration method which is combination of Variational Iteration method and Homotopy Perturbation Method. An example of the propagation of single soliton is given to show the precision of this method.

In the present paper, approximate analytical solutions for flow in unconfined aquifers with streams are obtained assuming one-dimensional horizontal groundwater flow in homogeneous and isotropic aquifer with recharge effect using variational homotopy perturbation method which is a combination of variational iteration method and homotopy perturbation method. The governing nonlinear Boussinesq equation is obtained by using a basic principle of conservation of mass followed by Dupuit's assumptions. Sensitivity of the parameters has been analyzed. The obtained approximate analytical solutions are numerically validated. The present analytical method is reliable and can be equally well applied to other nonlinear equations arising in the stream-aquifer interaction problems.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.