Generalized cofactors and nonlinear superposition principles

DOI10.1016/S0893-9659(03)90107-8zbMath1057.34002OpenAlexW2049853891MaRDI QIDQ1431993

Jaume Giné, Isaac A. García

Publication date: 11 June 2004

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(03)90107-8

zbMATH Keywords

transcendental solutionsplanar polynomial differential equationsnon-Liouvillian first integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (22)

Explicit non-algebraic limit cycles for polynomial systems ⋮ Formal Weierstrass integrability for a Liénard differential system ⋮ A survey on the inverse integrating factor ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ Formal Weierstrass Nonintegrability Criterion for Some Classes of Polynomial Differential Systems in ℂ2 ⋮ Weierstrass integrability in Liénard differential systems ⋮ On Liouvillian integrability of the first-order polynomial ordinary differential equations ⋮ A note on Liouvillian integrability ⋮ Integrability of planar polynomial differential systems through linear differential equations ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ Weierstrass integrability of differential equations ⋮ Darboux theory of integrability for a class of nonautonomous vector fields ⋮ The role of algebraic solutions in planar polynomial differential systems ⋮ On the Darboux integrability of Blasius and Falkner-Skan equation ⋮ Reduction of integrable planar polynomial differential systems ⋮ Abel differential equations admitting a certain first integral ⋮ Generalized nonlinear superposition principles for planar polynomial vector fields ⋮ Invariant curves and integrability of planar \(\mathcal C^r\) differential systems ⋮ Orbitally universal centers ⋮ An integrating factor of the Darboux differential systems ⋮ NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS ⋮ Puiseux integrability of differential equations

Cites Work

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• Equations de Pfaff algébriques
• The limit cycle of the van der Pol equation is not algebraic
• Algebraic solutions for polynomial systems with emphasis in the quadratic case
• On real analytic foliations and the center problem
• Nonlinear superposition
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• Local analytic integrability for nilpotent centers
• Reduction of Singularities of the Differential Equation Ady = Bdx
• The center-focus problem and reversibility

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