Invariant solutions to the Khokhlov-Zabolotskaya singular manifold equation and their application

DOI10.1016/S0034-4877(18)30020-XzbMath1398.35200OpenAlexW2792504352MaRDI QIDQ1801027

Aleksandra Lelito, Oleg I. Morozov

Publication date: 26 October 2018

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(18)30020-x

zbMATH Keywords

Lax representationinvariant solutionssymmetry reductionsKhZ equationKhZ singular manifold equation

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) KdV equations (Korteweg-de Vries equations) (35Q53) Bulk waves in solid mechanics (74J10)

Uses Software

• Jets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A natural geometric construction underlying a class of Lax pairs
• A unified approach to computation of integrable structures
• Geometry of jet spaces and integrable systems
• Symmetry properties of a nonlinear acoustics model
• Cartan's structure theory of symmetry pseudo-groups, coverings and multi-valued solutions for the Khokhlov-Zabolotskaya equation
• Cartan's structure of symmetry pseudo-group and coverings for the \(r\)-th modified dispersionless Kadomtsev-Petviashvili equation
• Stable-range approach to short wave and Khokhlov-Zabolotskaya equations
• Long-wave equation with free boundaries. I. Conservation laws and solution
• Symmetries, invariant solutions and conservation laws of the nonlinear acoustics equation
• On exact solutions of nonlinear acoustic equations
• Nonlinear Beltrami equation and \(\tau \)-function for dispersionless hierarchies
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• Group-invariant solutions of a nonlinear acoustics model
• Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra
• Symmetries of the Khokhlov-Zabolotskaya equation
• CONTACT GEOMETRY AND NON-LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS
• Nonclassical symmetry reductions and exact solutions of the Zabolotskaya–Khokhlov equation
• Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws
• On Two‐Dimensional Non‐Steady Motion of a Slender Body in a Compressible Fluid
• Symmetries and differential equations

This page was built for publication: Invariant solutions to the Khokhlov-Zabolotskaya singular manifold equation and their application