New analytical methods for cleaning up the solution of nonlinear equations

Analytical methods belong to perhaps the most challenging, promising, and `romanticʹ area of modern mathematics, and are playing an even more important role in the mathematics and other ramifications of science, prompting a resurgence of interest in the application of modern as well as classical or ancient mathematics to the search for approximate analytical solutions for various real-life nonlinear physical problems. MatLab and other mathematical software give rise to the tantalizing possibility of analytically seeking approximate solutions to specific problems and revealing various features of the series of solutions obtained.