Multidimensional partial differential equation systems: Nonlocal symmetries, nonlocal conservation laws, exact solutions
نویسندگان
چکیده
For systems of partial differential equations PDEs with n 3 independent variables, construction of nonlocally related PDE systems is substantially more complicated than is the situation for PDE systems with two independent variables. In particular, in the multidimensional situation, nonlocally related PDE systems can arise as nonlocally related subsystems as well as potential systems that follow from divergence-type or lower-degree conservation laws. The theory and a systematic procedure for the construction of such nonlocally related PDE systems is presented in Part I A. F. Cheviakov and G. W. Bluman, J. Math. Phys. 51, 103521 2010 . This paper provides many new examples of applications of nonlocally related systems in three and more dimensions, including new nonlocal symmetries, new nonlocal conservation laws, and exact solutions for various nonlinear PDE systems of physical interest. © 2010 American Institute of Physics. doi:10.1063/1.3496383
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