**Contact Information**

- leejh$\color{red}{@}$math.sinica.edu.tw
- +886 2 2368-5999 ext. 400
- +886 2 2368-9771

**Research Interests**

- Partial Differential Equations
- Inverse Scattering

**Education**

- Ph.D. Yale University (1978/9-1983/5 )
- B.S. National Taiwan University (1972/9-1976/6)

**Work Experience**

- 兼任教授 台灣大學/數學系 1996/9 - 2009/7
- (兼)副所長 中央研究院/數學研究所 1996/8 - 2000/7
- 研究員 Institute of Mathematics, Academia Sinica, R.O.C. 1995/09
- 兼任副教授 台灣大學/數學系 1988/9 - 1996/7
- part-time associate professor Inst. of Applied Math, Tsing-Hua Univ., Hsinchu 1983/8-1985/6 and 1986/8-1987/6
- 副研究員 中央研究院/數學研究所 1983/8 - 1995/8

**Research Descriptions**

Mr. Jyh-hao LEE obtained his Ph.D at Yale in 1983, then worked as associte research fellow since then. He was promoted as research fellow in 1995.Dr. Lee ever taught at the Institute of Applied Mathematics, National Tsing-Hua University. He taught at the Department of Mathematics, National Taiwan University from Fall 1988 to 2009 summer .

Dr. Lee's major research interests are the inverse scattering transform and the associated evolution equations and wavelet analysis. He is also interested in the differential equations and classical analysis.

Dr. Lee's research interest lies on P.D.E, integrable systems and soliton equations. He has worked on the analysis part for the AKNS-ZS system with quadratic, polynomial spectral parameters based on the set-up of Beals-Coifman.This involves the Riemann-Hilbert problem. He has been aware of many aspects related to Riemann-Hilbert problem. In the past decade, he has considered several integrable systems with "quantum potentials" (jointly with Oktay Pashaev).

A novel integrable version of the Nonlinear Schrodinger Equation (NLS) equation namely , $$i \frac{\partial \psi}{\partial t} + \frac{\partial^2 \psi}{\partial x^2} + {\Lambda \over 4} |\psi|^2 \psi = s \frac{1}{|\psi|}\frac{\partial^2 |\psi|}{\partial x^2} \psi, $$

has been termed the resonant nonlinear Schrödinger equation (RNLS)(also called Nonlinear Schrödinger equation with quantum potential ). It can be regarded as a third version of the NLS, intermediate between the defocusing and focusing cases. The critical value $s = 1$ separates two distinct regions of behaviour. Thus, for $s < 1$ the model is reducible to the conventional NLS, (focusing for $\Lambda > 0$ and defocusing for $\Lambda < 0$). However, for $s > 1$ it is not reducible to the usual NLS, but rather to a reaction-diffusion system, which can also be transform into Broer-Kaup system.

**Selected Publications**

*J. Plasma Physics*, 73 (part 2), 257-272, 2007.

*Teoret. Mat. Fiz.*, 152 (1), 133-146, 2007.

*Mathematics and Computers in Simulation*, 74 (4-5), 323-332, 2007.

*Theoret. and Mat. Fiz.*, 144 (1), 995-1003, 2005.

*Chaos, Solitons and Fractals*, 19, 109-128, 2004.

*proc. of Nonlinear Physics: Theory and Experiment,Gallipoli,World Sci.,2003*, 79-82, 2003.

*Modern Physics Letters A*, 17 (24), 1601-1619, 2002.

*Chaos, Solitons and Fractals*, 13, 1475-1492, 2002.

*THeor. Math. Phys.*, 2000.

*Proc. of 8th Workshop on Differential Equations Kaohsiung, Sun Yat-sen University*, Jan., 8-9, 2000.

*Chaos, Solitons & Fractals*, 11, 2193-2202, 2000.

*J. of Mathematical Physics*, 39 (1), 102-123, 1998.

*International J. of Modern Physics A*, 12 (1), 213-218, 1997.

*Physica D*, 81, 32-43, 1995.

*Theoretical and Mathematical Physics*, 99, 337-344, 1994.

*Theoretical and Mathematical Physics*, 99, 322-328, 1994.

*preprint*

*the Proc. of 21th International Conf. on the Differential Geometry Methods on the Theoretical Physic, Tianjin*, 1992-06.

*Clarkson University, Potsdam, New York, U.S.A.*, Aug., 1-11, 1991.

*The Transactions of the American Mathematical Society*, 316, 327-336, 1989.

*Chinese J. of Mathematics*, 16, 81-110, 1988.

*The Transactions of the American Mathematical Society*, 314, 107-118, 1989.

*Chinese J. of Mathematics*, 14, 225-248, 1986.

*Proc. of CCNAA-AIT Seminar on Differential Equations, Hsinchu, Taiwan*, 205-214, 1985-06.

*Chinese J. of Mathematics*, 12, 223-233, 1984.

*Ph.D Dissertation, Yale University*, 1983-05.

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, 2017 (13), 058-071-, 2017-07. (http://www.emis.de/journals/SIGMA/2017/058/)

*presented in 2015 Cross-Strait Joint Conference on Integrable Systems and Related Topics (and a colloq. talk in Quanzhou campus of HuaQiao Univ.)*, 2016-06.

*NSC(MOST) report(2014-2015)*, 2016-01.

*Prof. of 10th Taiwan-Philippines Symposium on Analysis, Mar. 30-April 3, 2014*, 2015-04.

*Journal of Physics: Conference Series (Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013))*, 482, 12026-0, 2014-03. (http://iopscience.iop.org/1742-6596/482/1)

*preprint*, 2013-06.

*Special Session 57: Nonlinear and Dispersive Partial Differential Equations,”The 9th AIMS Conference on Dynamical Systems, Differential Equations and Application,Orlando, Florida, USA, July1-5*, 2012-07.

*Chaos, Solitons and Fractals*, 45 (8), 1041-1047, 2012-08. (http://www.sciencedirect.com/science/article/pii/S0960077912001075)

*Chaos Solitons and Fractals*, 2012-04.

*7th IMACS conference on Nonlinear Evolution Equation and Wave Phenomena: Computation and Theory at Athens, Georgia, USA, April 4-7, 2011.*, 2011-12.

*Shanghai International Symposium on Nonlinear Science and Application, June 29-July 4, 2010, Xuzhou & Shanghai, China.*, 2010-10.

*proc. of 3rd International Conference on Nonlinear Science and Complexity,28-31 July, 2010, Ankara, Turkey*, 2010-10.

*Journal of Mathematical Physics*, 2009-12.

*Chaos, Solitons and Fractals*, 2009-04.

*J. Phys. A :Math. Theor.*, 41, 452001-0, 2008.

*Theoretical and Mathematical Physics.*, 160 (1), 987-995, 2009-06-30.