自然界和工程技术领域存在大量的非线性问题, 它们通常需要用非线性微分方程来描述.
守恒量在微分方程的求解, 约化和定性分析方面发挥重要作用. 因此, 研究非线性动力学方程的 …

In this paper, the approximate Noether theorems for approximate Birkhoffian systems are
presented and discussed. The approximate Birkhoff equations for the systems are …

The partial Hamiltonian systems of the form q ̇ i=∂ H∂ pi, p ̇ i=−∂ H∂ q i+ Γ i (t, qi, pi)
arise widely in different fields of the applied mathematics. The partial Hamiltonian systems …

We provide the Hamiltonian version of the approximate Noether theorem developed for the
perturbed ordinary differential equations (ODEs)(Govinder et al. in Phys Lett 240 (3): 127 …

We develop a new approach termed as a discount free or partial Lagrangian method for
construction of first integrals for dynamical systems of ordinary differential equations (ODEs) …

There are a lot of nonlinear problems in nature and engineering technology, which need to
be described by nonlinear differential equations. Conservation laws play an important role in …

The notions of artificial Hamiltonian (partial Hamiltonian) and partial Hamiltonian operators
are used to derive the first integrals for the first order systems of ordinary differential …

The approximate Noether theorem and its inverse theorem for the nonlinear dynamical
systems with approximate exponential Lagrangian and approximate power-law Lagrangian …

The approximate partial Noether theorem proposed earlier for the ordinary differential
equations (ODEs)(Naeem and Mahomed in Nonlinear Dyn 57 (1–2): 303–311, 2009) is …

This article investigates the first integrals and closed-form solutions of some nonlinear first-
order dynamical systems from diverse areas of applied mathematics. We use the notion of …