My research focuses on nonlinear waves (nonlinear PDEs) and their physical applications. Nonlinear waves are abundant in science and engineering. They include optical pulses in fibers, light beams in crystals and air, surface waves and internal waves in the ocean, and so on. This research has direct applications to fiber telecommunication systems, nonlinear optics and oceanography. One example is the concept of using optical solitons as information bits in data transmission, which is revolutionizing the telecommunication industry. Mathematically, nonlinear waves are described by nonlinear partial differential equations (PDEs). Some of these equations are integrable. Such equations have magic! Most others are not integrable. In such cases, both the numerical and analytical methods are important. This is a challenging field, and many discoveries are yet to be made.
Areas of Expertise and/or Research
Nonlinear Waves, Nonlinear Optics, Numerical Methods.
- Ph.D. (1994), Massachusetts Institute of Technology
Innovation Hall E442
- Math 19, Fundamentals of Calculus I
- Math 20, Fundamentals of Calculus II
- Math 124, Linear Algebra
- Math 230, Differential Equations
- Math 266, Chaos, Fractals and Dynamical Systems
- Math 271, Advanced Mathematics for Engineers and Scientists
- Math 330, Advanced Ordinary Differential Equations
- Math 339, Partial Differential Equations
- Math 395, Nonlinear Partial Differential Equations