On the isogroups of the semilinear hyperbolic equation \(u_{xt}=f(u)\) and its exact solutions for the case of the Liouville equation

DOI10.1016/0020-7225(92)90029-GzbMath0757.35040MaRDI QIDQ1199214

K. Vijayakumar, O. P. Bhutani

Publication date: 16 January 1993

Published in: International Journal of Engineering Science (Search for Journal in Brave)

zbMATH Keywords

Noether theoremnonlinear ordinary differential equationsimilarity solutionsorbital equationsclosed form exact solutioninfinitesimal Lie groupsinvariant groups of transformationisovector approachpotential principle

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Invariance and symmetry properties for PDEs on manifolds (58J70) Exterior differential systems (Cartan theory) (58A15) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (6)

On the generalized forms of exact solutions to the Liouville equation via direct approach ⋮ Similarity reductions and Painlevé analysis for the nonlinear Boltzmann equation ⋮ Isogroup classification of equations of meteorology ⋮ General solutions to the 2D Liouville equation ⋮ Isogroups and exact solutions for some Klein–Gordon and Liouville-type equations in n-dimensional Euclidean space ⋮ A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie-group method

Cites Work

• On the first integral of the nonlinear shallow-membrane equation via Noether's theorem
• Similarity methods for differential equations
• On the isogroups of the generalised diffusion equation
• A model unified field equation
• A Solvable Nonlinear Wave Equation
• The Bäcklund problem for the equation ∂2z/∂x1∂x2= f (z)
• On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance
• Prolongation structures of nonlinear evolution equations
• Nonlinear Meson Theory of Nuclear Forces. I. Neutral Scalar Mesons with Point-Contact Repulsion
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