本文综述了力学分析中对称性与守恒律的研究进展. 首先, 介绍了连续系统中的Lie 群对称性,
包括微分方程和偏微分方程的Lie 群对称性, 泛函的Lie 群对称性及其守恒律 …

We present the Lie symmetry analysis for the famous nonlinear equation describing chains
of atoms with long range interaction. We also study the conservation laws by computing the …

A detailed symmetry analysis is performed for a microscopic model used to describe traffic
flow in two-lane motorways. The traffic flow theory employed in this model is a two …

This paper reviews the research progress on symmetry and conservation laws in
mechanical analysis. It begins by introducing Lie group symmetries in continuous systems …

By applying the Lie symmetry method, group-invariant solutions are constructed for axially
loaded Euler beams. The corresponding mathematical models of the beams are formulated …

In this paper, we employ the time fractional higher order nonlinear Boussinesq–Burgers
system to investigate shallow water waves based on the Riemann–Liouville and Caputo …

This paper uses the classical Lie method to determine symmetry reductions and exact
solutions of the time-dependent Calogero-Bogoyavlenskii-Schiff equation (vCBS). This …

The propagation of nonlinear solitary and shallow water waves can be examined by
nonlinear evolution equations. The dynamics of nonlinear behavior are described by exact …

We investigate variational, Lie and Killing symmetries of the Lagrangian of an essential
class of four-dimensional (pseudo-) Riemannian manifolds, ie, non-reductive homogeneous …

This article introduces a mathematical model that utilizes a nonlinear differential equation to
study a range of phenomena such as nonlinear wave processes, and beam deflections …