Mathematical Physics, Integrable Systems, Nonlinear Waves, Soliton Theory

August 2000–Present, Teacher, Department of Mathematical Sciences and Teaching Center of Mathematics, Tsinghua University;

July 2001–October 2001, Assistant Researcher, City University of Hong Kong;

November 2001–January 2003, Postdoctoral Researcher, CEA-Saclay, France;

September 2005–March 2006, Visiting Scholar, University of California, San Diego, USA;

January 2010–April 2010, Visiting Professor, Complutense University of Madrid, Spain;

2001, Received the Second Prize for Outstanding Young Scholar Paper, Beijing Mathematical Society;

2017, Received the Second Prize for Beijing Higher Education Teaching Achievement (Ranked 4th of 6);

Led 2 National Natural Science Foundation of China (NSFC) projects (1 Young Scientist Fund, 1 General Program) and 1 NSFC-CNRS (France) Collaborative Project. Runliang Lin and collaborators have made significant contributions in constructing and solving new multi-component (2+1)-dimensional integrable systems, solving (1+1)-dimensional soliton equations with self-consistent sources, studying the continuous limit of discrete integrable systems, and deriving the Lax representation of discrete Painlevé equations. (1) Proposed a method for constructing and solving extended (2+1)-dimensional integrable systems, derived bilinear equations for the extended KP hierarchy, and obtained a simpler Hirota bilinear form for equations with sources (R.L. Lin, et al, Theor. Math. Phys., 2016). (2) Proposed a method using constrained systems and inverse scattering to solve (1+1)-dimensional soliton hierarchy with self-consistent sources, obtained explicit soliton solutions for the KdV hierarchy with self-consistent sources, advancing research in this area. The related paper (R.L. Lin, et al., Physica A, 2001) received the 2001 Beijing Mathematical Society Outstanding Young Scholar Paper Second Prize. (3) Clearly established the continuous limit relationship between the Toda hierarchy and the KdV hierarchy, proving a conjecture proposed by American scholar Gieseker in 1996 (R.L. Lin, et al, J. Phys. A, 2002). Representative Papers:

[1] Runliang Lin, Y.K. Du, Generalized Darboux transformation for the discrete Kadomtsev-Petviashvili equation with self-consistent sources, Theoretical and Mathematical Physics, 196(3): 1320-1332, (2018).

[2] Runliang Lin, H. Peng and M. Manas, The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons, J. Phys. A: Math. Theor., 43 (2010) 434022.

[3] Runliang Lin, R. Conte and M. Musette, On the Lax pairs of the continuous and discrete sixth Painlev\'e equations, J. Nonlinear Math. Phys., 10 (Suppl 2) (2003) 107-118.

[4] Runliang Lin, Yunbo Zeng and Wen-Xiu Ma, Solving the KdV hierarchy with self-consistent sources by inverse scattering method, Physica A, 291 (2001) 287-298.

Main Courses Taught: Calculus, Linear Algebra, among others

Published Textbooks: Linear Algebra and Geometry (Volumes 1 and 2) (2nd Edition), Zhengguang Yu, Ziqun Lu, Runliang Lin, Tsinghua University Press, 2015

Supervised 3 master’s students.