University of Central Florida STARS Electronic Theses and Dissertations, 2004-2019 2016 Building Lax Integrable Variable-Coefficient Generalizations to Integrable PDEs and Exact Solutions to Nonlinear PDEs Matthew Russo University of Central Florida Part of the Mathematics Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Doctoral Dissertation (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact
[email protected]. STARS Citation Russo, Matthew, "Building Lax Integrable Variable-Coefficient Generalizations to Integrable PDEs and Exact Solutions to Nonlinear PDEs" (2016). Electronic Theses and Dissertations, 2004-2019. 4917. https://stars.library.ucf.edu/etd/4917 BUILDING LAX INTEGRABLE VARIABLE-COEFFICIENT GENERALIZATIONS TO INTEGRABLE PDES AND EXACT SOLUTIONS TO NONLINEAR PDES by MATTHEW RUSSO B.S. University of Central Florida, 2012 M.S. University of Central Florida, 2014 A dissertation submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics in the College of Sciences at the University of Central Florida Orlando, Florida Spring Term 2016 Major Professor: S. Roy Choudhury c 2016 Matthew Russo ii ABSTRACT This dissertation is composed of two parts. In Part I a technique based on extended Lax Pairs is first considered to derive variable-coefficient generalizations of various Lax-integrable NLPDE hi- erarchies recently introduced in the literature. It is demonstrated that the technique yields Lax- or S-integrable nonlinear partial differential equations (nlpdes) with both time- and space-dependent coefficients which are thus more general than almost all cases considered earlier via other methods such as the Painleve´ Test, Bell Polynomials, and various similarity methods.