New symmetry solution techniques for first-order nonlinear PDEs.

DOI10.1016/S0096-3003(00)00085-0zbMath1162.35308OpenAlexW1987702743MaRDI QIDQ1855080

Yanyan Li

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(00)00085-0

zbMATH Keywords

Computer algebraSymmetryExterior differential systemFirst-order partial differential equationFrobenius integrable

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Geometric theory, characteristics, transformations in context of PDEs (35A30) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (4)

Unnamed Item ⋮ Solvable structures for evolution PDEs admitting differential constraints ⋮ Generalized Solvable Structures and First Integrals for ODEs Admitting an 𝔰𝔩(2, ℝ) Symmetry Algebra ⋮ \( \mathscr{C}^\infty \)-symmetries of distributions and integrability

Uses Software

• SYMMGRP
• DIMSYM
• CRACK
• LIE

Cites Work

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• Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. I
• Symmetries of distributions and quadrature of ordinary differential equations
• Integrability by quadratures for systems of involutive vector fields
• DIMSYM and LIE: Symmetry determination packages
• Sur les équations aux dérivées partielles du second ordre, \(F(x,y,z,p,q,r,s,t)=0\), intégrables par la méthode de Darboux
• Sur les équations aux dérivées partielles du second ordre, F(x,y,z, p,q,r,s,t)=0, intégrables par la méthode de Darboux. 2
• Geometric Aspects of Reduction of Order
• Solvable structures and hidden symmetries
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries
• Alternatives to the Cartan-Kähler theorem
• LIE, a PC program for Lie analysis of differential equations
• Solvable symmetry structures in differential form applications

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