報告人：George Bluman
題目：Nonlocally related systems: their construction and applications for PDE systems with two or more independent variables（I）
地點：1c102
時間👩⚖️：2012年5月3日13:00
摘要🦹🏻♀️：
It is shown how to construct systematically nonlocally related systems for a given PDE system. Such systems are not invertibly related to the given system, i.e, there are no 1:1 transformations connecting the systems. However, each solution of the given PDE system yields a solution of every nonlocally related system through connection formulas and the converse also holds, i.e., each solution of any nonlocally related system yields a solution of the given PDE system through a connection formula. Illustrative examples will include nonlinear wave equations, nonlinear telegraph equations and planar gas dynamics equations. In particular, nonlocal symmetries for each of these systems will be exhibited through nonlocally related systems. Systematic methods to construction such nonlocally related systems arise naturally through the local conservation laws, subsystems and point symmetries of the given PDE system.The situation in the case of three or more independent variables is especially interesting. Here it will be shown that the use of conservation laws to obtain nonlocally related systems must be augmented by gauge constraints.
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