On a general solution of a nonlinear 2-system of the form \(x^ 2\) dw/dx = Lambda w + xh(x,w) with a constant diagonal matrix Lambda of signature (1,1)

DOI10.2748/TMJ/1178229532zbMath0471.34007OpenAlexW2042586808MaRDI QIDQ1157443

Masahiro Iwano

Publication date: 1980

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229532

zbMATH Keywords

asymptotic expansions

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25)

Related Items (4)

Doubly-resonant saddle-nodes in \(\mathbb {C}^{3}\) and the fixed singularity at infinity in the Painlevé equations: formal classification ⋮ Doubly-resonant saddle-nodes in (\protect \mathbb{C}^3,0) and the fixed singularity at infinity in Painlevé equations: analytic classification ⋮ On a general solution of a nonlinear n-system of the form \(x^ 2\) dy/dx = (\(1_ n(\)mu) + \(x1_ n(\)alpha))y + xf(x,y) with a constant diagonal matrix \(1_ n(\)mu) of signature (m,n-m) ⋮ On an n-parameter family of solutions of a nonlinear n-system with an irregular type singularity

Cites Work

• Intégration analytique d'un système d'équations différentielles non linéaires dans le voisinage d'un point singulier. I, II
• On general solution of a first-order non-linear differential equation of the form x(dy/dx)=y(lambda+f(x,y)) with negative rational lambda(*)
• Analytic integration of a system of nonlinear ordinary differential equations with an irregular type singularity. I
• Analytic integration of a system of nonlinear ordinary differential equations with an irregular type singularity. II
• Analytic expressions for bounded solutions of non-linear ordinary differential equations with an irregular type singular point
• A general solution of a system of nonlinear ordinary differential equations \(xy'=f(x,y)\) in the case when \(f^ y(0,0)\) is the zero matrix
• Sur l'étude analytique des solutions d'un système d'équations différentielles dans le voisinage d'un point singulier d'indetermination. 1
• Sur l'étude analytique des solutions d'un système d'équations différentielles dans le voisinage d'un point singulier d'indetermination. 2
• Sur l'étude analytique des solutions d'un système d'équations différentielles dans le voisinage d'un point singulier d'indetermination. 3
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