A Hamiltonian approach to the cohomogeneity one Ricci soliton equations and explicit examples of non-Kähler solitons by Betancourt de la Parra, A, Dancer, A, Wang, M

“…We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not of Kahler type in five dimensions.…”

Pembinaan persamaan Korteweg-de Vries sebagai sistem Hamiltonan bermatra tidak terhingga by Abdul Aziz, Zainal

“…We construct the Korteweg-de Vries equation (pKdV) as an infinite dimensional Hamiltonian system. In particular, this result is derived consequently from the fact that the pKdV's dynamical system exists in a weak symplectic manifold. …”
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Limit cycles in piecewise smooth perturbations of a quartic isochronous center by Haifeng Song, Linping Peng, Yong Cui

“…This article concerns the bifurcation of limit cycles from a quartic integrable and non-Hamiltonian system. By using the first order averaging method and some mathematical technique on estimating the number of the zeros, we show that under a class of piecewise smooth quartic perturbations, seven is a lower and twelve an upper bound for the maximum number of limit cycles bifurcating from the unperturbed quartic isochronous center.…”
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Energy diffusion and absorption in chaotic systems with rapid periodic driving by Wade Hodson, Christopher Jarzynski

“…When a chaotic, ergodic Hamiltonian system with N degrees of freedom is subject to sufficiently rapid periodic driving, its energy evolves diffusively. …”
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Langevin equation with colored noise for constant-temperature molecular dynamics simulations. by Ceriotti, M, Bussi, G, Parrinello, M

“…Since the equations of motion are linear in nature, it is easy to predict the response of a Hamiltonian system to such a thermostat and to tune at will the relaxation time of modes of different frequency. …”

The crease flow on null hypersurfaces by Spiros Cotsakis

“…Abstract The crease flow, replacing the Hamiltonian system used for the evolution of crease sets on black hole horizons, is introduced and its bifurcation properties for null hypersurfaces are discussed. …”
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Two discrete models for semi-geostrophic dynamics by Baigent, S, Norbury, J

“…The first model, the lattice model, gives rise to a Hamiltonian system for which the Hamiltonian vector field is discontinuous. …”

Emergent Spacetime and Cosmic Inflation by Hyun Seok Yang

“…The emergent spacetime picture admits a background-independent formulation so that the inflation is described by a conformal Hamiltonian system which requires neither an inflaton field nor an ad hoc inflation potential. …”
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MGPS: Midpoint-Series Group Preserving Scheme for Discretizing Nonlinear Dynamics by Zhenxing Xu, Jinzhao Wu

“…Meanwhile, it works well with the periodic Hamiltonian system.…”
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Periodic solutions to a class of distributed delay differential equations via variational methods by Xiao Huafeng, Guo Zhiming

“…We transform the search for periodic solutions with the special symmetry of a delay differential equation to the problem of finding periodic solutions of an associated Hamiltonian system. Using the critical point theory and the pseudo-index theory, we obtain some sufficient conditions for the multiplicity of periodic solutions. …”
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Position and momentum operators for a moving particle in bulk by Wu-zhong Guo

“…The dynamics of the particle, i.e., the geodesic equation, can be formulated as a Hamiltonian system with canonical variables. The achievements of our paper are to construct the dual CFT states and the operators corresponding to the canonical variables. …”
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Self-Learning Machines Based on Hamiltonian Echo Backpropagation by Víctor López-Pastor, Florian Marquardt

“…We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. It relies on implementing a time-reversal operation and injecting a small error signal on top of the echo dynamics. …”
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Bifurcations of traveling wave solutions for the mixed Korteweg-de Vries equation by Hui Wang, Xue Wang

“…Under different parameter conditions, the bifurcation curves and phase portraits of corresponding Hamiltonian system are given. Furthermore, many different types of exact traveling waves are obtained, which include hyperbolic function solution, triangular function solution, rational solution and doubly periodic solutions in terms of the Jacobian elliptic functions. …”
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Uncomputability and Physical Law by Lloyd, Seth

“…In particular, the form of the energy spectrum of quantum systems capable of universal computation is uncomputable: to answer whether a Hamiltonian system is gapped or gapless in a particular sector requires one to solve the Halting problem. …”
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Examples of mirror partners arising from integrable systems by Hausel, T, Thaddeus, M

“…The special Lagrangian tori come from an algebraically completely integrable Hamiltonian system: the Hitchin system.…”

Quantum phase transition between cluster and antiferromagnetic states by Son, W, Amico, L, Fazio, R, Hamma, A, Pascazio, S, Vedral, V

“…We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. …”

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics by Ilon Joseph

“…This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. …”
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Periodic orbits, superintegrability, and Bertrand’s theorem by R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito

“…Periodic orbits are the key for understanding classical Hamiltonian systems. As we show here, they are the clue for understanding Bertrand’s result relating the boundedness, flatness, and periodicity of orbits with the functional form of the potentials producing them. …”
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一个阿贝尔积分根的数目的下界(A lower bound for the number of zeroes about an Abelian integral) by YANDong-mei(严冬梅), LÜDa-mei(吕大梅)

“…In this paper, we study a polynomial near-Hamiltonian system , , where H(x, y) = y2/2+ x2k/(2k), k≥1. …”
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Soliton solutions and dynamics analysis of fractional Radhakrishnan–Kundu–Lakshmanan equation with multiplicative noise in the Stratonovich sense by Chen Peng, Zhao Li

“…Firstly, the wave transformation is used to obtain the nonlinear ordinary differential equation, and then the nonlinear ordinary differential equation is transformed into a two-dimensional plane dynamic system with a Hamiltonian system. Secondly, the phase portrait and sensitivity of the plane dynamic system and its perturbed system are studied using Maple software. …”
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