A non-linear diffusion problem with power-law diffusivity: An approximate solution experimenting with a modified sinc function

Employing a modified version of the cardinal $Sinc_{\pi} \left(\pi x^{n} \right)$ function as the assumed profile, the work presents approximate solutions of a non-linear (degenerate) diffusion equation with a power-law-type concentration-dependent diffusivity in a semi-infinite domain by the integral-balance method (double integration technique). The behavior and basic features of a modified function $ Sinc_{\pi}\left(x^{n} \right)$ are addressed, highlighting how it is used in the generated approximate solutions. It has been successful in implementing the concept of the modified $sinc (x)$ function's variable (argument-dependent) exponent. To demonstrate the suitability of the suggested technique, comparative examinations concerning well-known approximate analytical and numerical problem solutions have been developed.