Reduction of nonhomogeneous quasilinear 2×2 systems to homogeneous and autonomous form

DOI10.1063/1.2992482zbMath1152.81390OpenAlexW2013143088MaRDI QIDQ5505081

Carmela Currò, Francesco Olivieri

Publication date: 23 January 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2992482

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (12)

Symmetry of stochastic non-variational differential equations ⋮ Variants of the Hodograph Method for Solving a System of Two Quasilinear Equations ⋮ A consistent approach to approximate Lie symmetries of differential equations ⋮ Lie group analysis and Riemann problems for a \(2\times 2\) system of balance laws ⋮ Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones ⋮ Equivalence transformations of quasilinear first order systems and reduction to autonomous and homogeneous form ⋮ Reduction of balance laws in \((3+1)\)-dimensions to autonomous conservation laws by means of equivalence transformations ⋮ Construction of autonomous conservation laws ⋮ Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs ⋮ Unsteady solutions of Euler equations generated by steady solutions ⋮ Reduction of balance laws to conservation laws by means of equivalence transformations ⋮ Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives

Cites Work

• Unnamed Item
• Influence of a strong discontinuity on the propagation of second order discontinuities
• Group analysis and constitutive laws for fluid filled elastic tubes
• Reduction to linear canonical forms and generation of conservation laws for a class of quasilinear hyperbolic systems
• Acceleration wave propagation in hyperelastic rods of variable cross- section
• On the influence of initial conditions on the motion of water confined within a tank
• Linearization procedure of nonlinear first order system of partial differential equations by means of canonical variables related to Lie groups of point transformations
• A linearization procedure for quasilinear non-homogeneous and non-autonomous \(2\times 2\) first-order systems
• How to build up variable transformations allowing one to map nonlinear hyperbolic equations into autonomous or linear ones
• Exact Solutions for Large Amplitude Waves in Dispersive and Dissipative Systems
• Some Applications of the Riemann Method to Electromagnetic Wave Propagation in Nonlinear Media
• A class of linearizable models and generation of material response functions to nonlinear hyperbolic heat conduction
• When Nonlinear Differential Equations are Equivalent to Linear Differential Equations
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Wave features of a class of reducible nonhomogeneous and nonautonomous models
• When nonautonomous equations are equivalent to autonomopus ones
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations

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