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In this paper a unified approach for finding soliton solutions is applied to the modified Fornberg-Whitham equation. Variety of peakon, periodic, and solitary new exact solutions are constructed.

In this paper, we expand the scope of application of the modified variational iteration method (MVIM) to solve the Impenetrable Agar Model Problem. This model represents the propagation of a bacterial exo-enzyme within an impenetrable host material which simulates the manifestations bacteria do on tissue wounds in an infection. The numerical results show that the MVIM is convenient, efficient, and easy to use for the model problem.

Starting with magnetohydrodynamic (MHD) equilibria for plasma field, and under certain conditions these MHD equations were reduced to a single nonlinear elliptic equation for magnetic potential ũ , known as Grad-Shafranov equation. By specifying the arbitrary functions in this equation, the Bullough-Dodd equation was obtained. Travelling wave solutions were given which turned out to be a very unimportant special case. In this paper, we give exact solutions using rational sech-csch functions.