Abstract
In this article, we successfully construct various kinds of exact
traveling wave solutions like, hyperbolic (kink and singular kink-shaped
soliton), trigonometric (periodic and singular periodic) as well as
rational function solutions for the best known mixed hyperbolic-elliptic
system of conservation laws, namely the van der Waals gas system in the
viscosity-capillarity regularization version by means of
($\frac{G’}{G^2}$)-expansion and advanced
$\mbox{e}^{-\phi(\tau)}$-expansion
functions methods. These techniques are very useful and exceptionally
helpful in a contrast with other analytical schemes, which show the
effectiveness and the simplicity to discuss the exact solutions. 3D and
contour figures are sketched in order to understand the physical
movement of the gained results under the selections ofunknown
parameters.