In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth th...

I n July, the European Commission approved the marketing of gefitinib (Iressa) for selected patients with non-small cell lung cancer, a milestone for a drug whose ups and downs have reflected the sometimes difficult road toward per-sonalized medicine in oncology. The key ingredient in the commis-sion's approval is patient selection–the proviso that gefi tinib be used only in patients with certa...

We investigate water infiltration pressure for hydrophobic nanochannels through molecular dynamics simulations. It is found that the entrance energy barrier significantly raises the infiltration pressure, which makes the classic Young-Laplace equation invalid for nanochannels. As the channel surface is tuned from superhydrophobic to hydrophobic, the infiltration pressure is greatly reduced main...

The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for ex...