Multidimensional partial differential equation systems: Nonlocal symmetries, nonlocal conservation laws, exact solutions
Copyright policy )Multidimensional partial differential equation systems: Nonlocal symmetries, nonlocal conservation laws, exact solutions
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.
- University of British Columbia Canada
- University of Saskatchewan Canada
Systems of nonlinear higher-order PDEs, Systems of linear higher-order PDEs, Existence problems for PDEs: global existence, local existence, non-existence, Symmetries, invariants, etc. in context of PDEs
Systems of nonlinear higher-order PDEs, Systems of linear higher-order PDEs, Existence problems for PDEs: global existence, local existence, non-existence, Symmetries, invariants, etc. in context of PDEs
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).17 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!