Dissipative forces play an important role in problems of classical as well as quantum
mechanics. Since these forces are not among the basic forces of nature, it is essential to …

Classical dynamical systems close to a critical point are known to act as efficient sensors
due to a strongly nonlinear response. We explore such systems in the quantum regime by …

We present a direct approach to the construction of Lagrangians for a large class of one-
dimensional dynamical systems with a simple dependence (monomial or polynomial) on the …

Classical Hamiltonian systems with balanced loss and gain are considered in this review. A
generic Hamiltonian formulation for systems with space-dependent balanced loss and gain …

Conservation laws for systems of exponential, power-law and logarithmic non-standard
Birkhoffian with fractional derivatives are investigated respectively, and their relationships …

We start with a self-contained brief review of the construction of non-standard Lagrangian
and Hamiltonian structures for the Liénard equations satisfying Chiellini condition, we apply …

Two mathematical physics' approaches have recently gained increasing importance both in
mathematical and in physical theories:(i) the fractional action-like variational approach …

We construct integrals of motion for several models of the quantum damped oscillators in a
framework of a general approach to the time-dependent Schrödinger equation with variable …

The Noether theorem and its inverse theorem for the nonlinear dynamical systems with
nonstandard Lagrangians are studied. In this paper, two kinds of nonstandard Lagrangians …

Recently, non-standard Lagrangians (NSL) have gained an increasing significance due to
their wide implications in the theory of non-linear differential equations, complex dynamical …