In my talk, I will introduce peakon equations and present a basic approach how to get peakon solutions. Those equations include the well-known Camassa-Holm (CH), the Degasperis-Procesi (DP), and other new peakon equations. Interesting thing is that an integrable equation may have W/M-shape solitons. In the talk, I will illustrate this feature through two new integrable equations that we found recently. Later, I take the CH case as a typical example to show how we obtain the peaked solitons.
My brief introduction: Fudan University, Institute of Mathematics, Ph. D (Applied Math), 1997. Ph D Advisors: Profs. Chaohao Gu and Hesheng Hu； One of the first hundred excellent Ph D dissertations awarded in 1999. Academic Appointments Tenured Professor, Dept of Math, UTPA, present. Researcher, Los Alamos National Laboratory (LANL), Theoretical Division, 2001-2004. Humboldt Research Fellow, Dept of Math, University of Kassel, Germany, 1999-2001. Professor, Liaoning University, Department of Mathematics, 1996-2001. Three current US grants over $1,330K, 2 books and over 110 publications in peer-reviewed international journals. University Faculty Excellence Award in research.