PROLONGATION STRUCTURES OF NONLINEAR SYSTEMS IN HIGHER DIMENSIONS |
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| Authors: | WU Ke CUO Han-ying WANG Shi-kun |
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| Institution: | 1. Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735, Beijing, China;
2. Institute of Applied Mathematics, Academia Sinica, P.O. Box 300, Beijing, China |
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| Abstract: | It is shown that the prolongation structure theory for nonlinear (evolution) equations with two independent variables can be generalized to the systems with many independent variables. By means of the nonlinear realization theory of gauge symmetries, the fundamental equations for prolongation structures and the requirements for the generalized Lax representations of the nonlinear systems in higher dimensions have been given. Based upon the invariances of the prvlongation structures or the generalized Lax representation under certain transformations, the general condition satisfied by the auto-Backlund transformations has been proposed and searching for a kind of auto-Backlund transformations has been transferred to solving the regular Riemann-Hilbert problem. |
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