6 papers · 1 filter
New solitary wave and Multiple soliton solutions of (3 + 1)-dimensional KdV type equation by using Lie symmetry approach
Sachin Kumar, Dharmendra Kumar
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite…
Lie symmetry analysis and new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation
Sachin Kumar, Dharmendra Kumar
Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this art…
PT-symmetric potentials with imaginary asymptotic saturation
Zafar Ahmed, Sachin Kumar
We point out that PT-symmetric potentials having imaginary asymptotic saturation: are devoid of scattering states and spe…
Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials
Zafar Ahmed, Sachin Kumar, Dona Ghosh
For complex PT-symmetric scattering potentials (CPTSSPs) , we show that c…
1-Multisoliton and other invariant solutions of combined KdV - nKdV equation by using symmetry approach
Sachin Kumar, Dharmendra Kumar
Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV e…
Pearson's correlation coefficient in the theory of networks: A comment
Zafar Ahmed, Sachin Kumar
In statistics, the Pearson correlation coefficient determines the degree of linear correlation between two variables and it is known that . In the t…