ABSTRACT

Many of the most interesting phenomena (e.g., singularity, stability, chaos, and solitons) are related to nonlinear PDEs [e.g., see Ablowitz and Clarkson (1991), Logan (1994), Taylor (1996), Debnath (2005), Galaktionov and Svirshchevskii (2006), and Kudryashov (2010d)]. However, the understanding of these phenomena required such technology that was either not available or limited in the pre-modern era. In modern mathematics, there exist computers, supercomputers, computer algebra systems (such as Maple and Mathematica), and an interactive programming environment for scientific computing, MATLAB, that can perform various mathematical operations of which humans are incapable and where symbolic and numerical computations play a central role in scientific progress [see Akritas (1989), Calmet and van Hulzen (1983), Davenport, Siret, and Tournier (1993), and Wester (1999)].