Partial Differential Equations with Applications

<p>Differential equations are essential for describing a real-world system as a mathematical model. Particularly it is well known that partial differential equations are used extensively in physics and engineering where problems involve functions of several variables such as the propagation of heat or sound fluid flow elasticity etc. Over the last few years a wide variety of methods have been developed to find analytical solutions to partial differential equations. Currently symmetry methods are intensively applied to solve partial differential equations obtaining exact analytic solutions. Additionally finding conservation laws or conserved quantities plays an important role in the solution of a problem. Furthermore there has been considerable research on Painlevé-type equations since 1980. Specifically Painlevé tests have been shown to be remarkable in their ability to predict whether an equation is integrable.</p>