Conservation laws of nonlinear PDEs arising in elasticity and acoustics in Cartesian, cylindrical, and spherical geometries
Year: 2025
Type: article
Abstract: Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave propagation in a circular cylinder and a cylindrical annulus. Next, using the multiplier method, conservation laws are derived for a parameterized system of constitutive equations in cylindrical coordinates involving a general expression for the Cauchy stress. Conservation laws for the Khokhlov-Zabolotskaya-Kuznetsov equation and Westervelt-type equations in various coordinate systems are also presented. To appear in Open Communications in Nonlinear Mathematical Physics. Special Issue in Honor of George W. Bluman, 2025 (27 pages, 6 tables, 54 references)
DOI: 10.46298/ocnmp.17124
Authors: Willy Hereman, Rehana Naz
Institution: Colorado School of Mines
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417453615
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