Applications of a new function introduced by Kudryashov [Optik. 2020;206:163550] to obtain solitary wave solutions of nonlinear PDEs through their travelling wave reductions are considered. The Kudryashov function, R, satisfying a first-order second degree ODE has several features which significantly assist symbolic calculations, especially for highly dispersive nonlinear equations. A remarkable feature of the Kudryashov function R, is that its even order derivatives are polynomials in R only while its odd order derivatives turn out to be polynomials in R and R_z . The procedure has been illustrated by means of the Schrödinger–Hirota equation, a quartic NLS equation and the fifth-order Kawahara equation as examples. A comparison with the Rayleigh–Ritz variational approach has also been considered for the purposes of illustration. The results obtained here are novel and span the family of solutions for such kind of equations.

The stabilization of Rayleigh-Taylor (RT) instability is investigated in a non-Newtonian unmagnetized dusty plasma with an experimentally verified model of shear flow rate dependent viscosity. It has been found that non-Newtonian property has also a significant role in stabilization of RT instability along with velocity shear stabilization in the short wavelength regime. The effect of the non-Newtonian parameters is more profound in the higher velocity shear rate regime. A detailed study is reported on the role of non-Newtonian effect on RT instability with conventional dust fluid equations using standard numerical eigenvalue analysis.