Integrability conditions for systems of two equations of the form \(u_ t=A(u)u_{xx}+F(u,u_ x)\). I

DOI10.1007/BF01033520zbMath0592.35087OpenAlexW1989140129WikidataQ61835435 ScholiaQ61835435MaRDI QIDQ1075522

A. B. Shabat, Alexander V. Mikhailov

Publication date: 1985

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01033520

zbMATH Keywords

nonlinear equationssystem reductionnontrivial conservation laws

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Nonlinear higher-order PDEs (35G20) Other special methods applied to PDEs (35A25)

Related Items (8)

On the integrability of systems of second order evolution equations with two components ⋮ Non-abelian evolution systems with conservation laws ⋮ Fundamental representations of the m-principal realization of g l∞ ⋮ The coupled modified Korteweg–de Vries equations: Similarity reduction, Lie–Bäcklund symmetries and integrability ⋮ Symmetries of Differential Equations and the Problem of Integrability ⋮ Investigating the exact integrability of the multiwave nonlinear Schrödinger equation ⋮ On a class of Toda chains ⋮ Integrability conditions for a certain class of nonlinear evolution equations and Kähler geometry

Cites Work

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• Nonlinear Schrödinger equations and simple Lie algebras
• Statistics of integral convex polygons
• New Integrable Nonlinear Evolution Equations
• Prolongation structures of nonlinear evolution equations
• Prolongation structures of nonlinear evolution equations. II
• A simple model of the integrable Hamiltonian equation
• Integrals of nonlinear equations of evolution and solitary waves

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