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Research group of mathematical physics in the Department of Shanghai Jiao Tong University focus on the theories and applications of integrable systems. A central topic in the study is to understand integrability for a large of nonlinear PDEs, nonlinear ODEs, nonlinear differential-difference equations and nonlinear difference equations. Those nonlinear equations possess rich mathematical structures,such as the Lax representations, the Hamiltonian structures, infinitely many conservation laws, sym-metries and multi-soliton solutions. They also have wide physical applications, such as water waves,hydromagnetic waves, nonlinear optics, plasma physics, field theory, quantum field. The theory of integrable systems is closely related to many mathematical areas, e.g., PDEs, ODEs, Lie group, Lie algebra, differential geometry, computational mathematics.

• Continuous and discrete integrable systems
• B¨acklund and Darboux transformations
• Bilinear formalism
• Hamiltonian systems
• Constructions of multisolitons and solitary wave interactions and collisions
• Painleve equations
• Special functiions and orthogonal polynomials and integrable systems
• Geometry theory in integrable systems
• Wave phenomena in the atmosphere and the ocean

• Chun-li Chen
• Guo-fu Yu
• Zuo-nong Zhu