Logo Logo

Resarch Summary

I am an applied mathematician with research interests in the analysis of climate data and theory of nonlinear waves. Error estimation of the climate data and uncertainty quantification of the climate change assessment are the focus of my research. Our spectral optimal averaging (SOA) method for inhomogeneous fields and our findings of multiple solutions of forced nonlinear waves have influenced the international community's research in the relevant fields. The United Nations’ Inter-governmental Panel for Climate Change (IPCC) adopted our SOA theory to quantify the uncertainty in global warming assessment (IPCC Report 2001, Figures 2.7 and 2.8). The report cited six of our papers. I have published 3 books and over 80 papers including a paper in Nature Geoscience. I have been personally recognized with international honors and awards, such as the prestigious US National Academy of Science’s NRC Associateship award in 1999 and the Chinese Academy of Sciences’ honor of “Well-known Overseas Chinese Scholar” in 2001. I was elected as President-elect of the Canadian Applied and Industrial Mathematics Society in 1999, and Vice-President of the Canadian Mathematical Society in 2003. My research team has been supported by more than 20 agencies, including NSF, NSERC, and NOAA. This summary describes my past research achievements and their significance.

A Major Multi-Institution NSF EaSM-3 Project Led By Yongkang Xue, UCLA, 2014-2018

1. New methods and theories for analyzing the climate and agroclimate data

My group has been conducting climate data analysis research in collaboration with distinguished climatologists since 1988. We have published a series of high-quality papers on the analysis of both observed data and model output.

2. Fluid Dynamics and Forced Nonlinear Waves

Before 1994, my group was mainly investigating the waves modeled by forced evolution equations, such as the forced Korteweg-de Vries (fKdV) equations, forced nonlinear Schrodinger equations and forced sine-Gordon equations. The mathematical difficulty of this research results from the lack of the group symmetries associated with unforced problems due to the non-conservation of momentum or other quantities. There exist some surprising phenomena, such as periodic upstream soliton radiation, and hydraulic fall in the fKdV equations, which do not occur in the unforced cases.  The mathematical community has recognized the importance of our research in this direction. In 1997, the American Mathematical Society held a special session on nonlinear waves, with emphasis on forced evolution equations. Our results attracted the attention of many leading researchers in PDE and nonlinear waves, such as Ted Wu, David McLaughlin, Jerry Bona, Mark Ablowitz, and Peter Lax.

3. Press Release on the Research Results from Sam Shen’s Group