Related papers: Explicit K-symplectic methods for nonseparable non…
In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and many researchers have been concerned with the design and analysis of numerical methods for solving oscillatory problems. In…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry,…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the…
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model…
The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables $[X, P,…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to…
In order to describe the impact of different geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we first define a kind of controlled magnetic Hamiltonian (CMH) system, and give a…
Recent well-posedness results have identified the Hardy space $L^2_+$ as the natural phase space for continuum Calogero-Moser models, both focusing and defocusing, on the line and on the torus. In this paper, we introduce a symplectic form…