Conservation laws of nonlinear PDEs arising in elasticity and acoustics in Cartesian, cylindrical, and spherical geometries
Willy Hereman, Rehana Naz
TL;DR
This paper derives conservation laws for nonlinear PDEs in elasticity and acoustics across Cartesian, cylindrical, and spherical geometries, using scaling and multiplier methods to analyze models in different coordinate systems.
Contribution
It introduces new conservation laws for nonlinear PDEs in elasticity and acoustics using scaling homogeneity and multiplier techniques across various geometries.
Findings
Conservation laws for shear wave propagation in cylinders and annuli.
Derived conservation laws for the Khokhlov-Zabolotskaya-Kuznetsov and Westervelt equations.
Application of methods across multiple coordinate systems.
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.
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