This is a one.year collaborative research project with Dr. Blake Temple, University of California at Davis and Dr. Randall Leveque, University of Washington working with Professor Wang Jinghua, Institute of Systems Science, Academia Sinica and Professor Lin Longwei, Zhongshan University, to study nonlinear waves using numerical and analytical methods. This project studies an important field of applied mathematics. The U.S. group is known for its work on the hyperbolic systems of conservation laws. The Chinese team has made significant progress in the area of wave interactions and large time step methods. Both areas are needed for understanding nonlinear waves, and jointly they can advance this field of applied mathematics.