B. Mayil Vaganan

New exact explicit solutions of the generalized KdV equations

Abstract As KdV equations are characterized by the Painleve equations we show here that generalized KdV equations are characterized by Euler–Painleve equations. A plethora of exact, explicit similarity solutions are found which include inverse of hypergeometric function.

Similarity solutions of the Burgers equation with linear damping

Abstract The Burgers equation with linear damping has been subjected to Lies group theoreticmethod of infinitesimal transformation to derive its solutions. To the best of our knowledge, we are the first to obtain a new similarity variable for an equation of the Burgers type and therefore provide new solutions.

Cauchy-Euler model, cellular automata simulation of the rate of recovery of the infected airway from COPD

Chronic obstructive pulmonary disease (COPD) is associated with the respiratory system. COPD is often treated with inhalers whose two major ingredients are the bronchodilators and the steroids. In this paper we mathematically model the deposition of the inhaled drug on the infected airway into Cauchy-Euler differential equation and use Visual Basic to simulate the evolution of the recovery of the inflamed airway.

Exact and explicit solutions of Euler–Painlevé equations through generalized Cole–Hopf transformations

Abstract More general Euler–Painleve equations are exactly linearized using generalized Cole–Hopf transform and are shown to admit exact solutions in terms of Kummer functions. The asymptotic behaviours of Euler–Painleve equations are also derived.