Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones

Abstract

A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear form is performed by constructing the canonical variables associated to the Lie point symmetries admitted by the nonlinear system. Some applications to relevant partial differential equations are given.

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Acknowledgments

Work supported by “Gruppo Nazionale per la Fisica Matematica” (G.N.F.M.) of the “Istituto Nazionale di Alta Matematica” (I.N.d.A.M.).

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Correspondence to Francesco Oliveri.

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Gorgone, M., Oliveri, F. Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones. Ricerche mat 66, 51–63 (2017). https://doi.org/10.1007/s11587-016-0286-8

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Keywords

  • Lie point symmetries
  • Quasilinear PDEs
  • Monge–Ampère equations

Mathematics Subject Classification

  • 35A30
  • 58J70
  • 58J72