대한수학회지 (Journal of the Korean Mathematical Society)

  • 제40권3호
  • /
  • Pages.517-561
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  • 2003
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS

  • 발행 : 2003.05.06
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초록

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in $\mathbb{C}$. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.

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참고문헌

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피인용 문헌

  1. New extension phenomena for solutions of tangential Cauchy–Riemann equations vol.41, pp.6, 2016, https://doi.org/10.1080/03605302.2016.1180536
  2. Lie symmetries and CR geometry vol.154, pp.6, 2008, https://doi.org/10.1007/s10958-008-9201-5
  3. Characterization of the Newtonian Free Particle System in $m\geqslant 2$ Dependent Variables vol.92, pp.2, 2006, https://doi.org/10.1007/s10440-006-9064-z