Exact solutions of the stochastic fractional long–short wave interaction system with multiplicative noise in generalized elastic medium by Tianyong Han, Zhao Li, Kun Zhang

“…In this study, the bifurcation and the influence of random interaction on the exact solution of the stochastic fractional long–short wave interaction system (SFL-SWIS) with multiplicative Brownian motion are studied, where the derivative refers to the modified Riemann–Liouville definition. After the Hamiltonian system is established by traveling wave transformation and first-order integration, we obtain abundant exact parametric solutions of SFL-SWIS. …”
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Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity by Hongxing Zhang, Naying Zhou, Wenfang Liu, Xin Wu

“…Since such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed, explicit symplectic integrators for the Kerr-type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. …”
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Robust and Safe Autonomous Navigation for Systems With Learned SE(3) Hamiltonian Dynamics by Zhichao Li, Thai Duong, Nikolay Atanasov

“…This paper develops a neural ordinary differential equation network to learn the dynamics of a Hamiltonian system from trajectory data. The learned Hamiltonian model is used to synthesize an energy-shaping passivity-based controller and analyze its <italic>robustness</italic> to uncertainty in the learned model and its <italic>safety</italic> with respect to constraints imposed by the environment. …”
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Cohomogeneity one Ricci solitons by de la Parra, A

“…</p> <p>In Chapter 3 we reformulate the cohomogeneity one Ricci soliton equation as a Hamiltonian system with constraint. We obtain a conserved quantity for this system and produce explicit formulas for solitons of dimension 5.…”

Pollutant dynamics in a subterranean estuary (Waquoit Bay, MA, USA) via mathematical modeling by Fareeha Sami Khan, M. Khalid, Ali Hasan Ali, Omar Bazighifan, F. Ghanim

“…The main objective of this paper is to develop a mathematical model to assess the situation of pollution in Waquoit Bay and suggest some solutions using optimal control theory with Hamiltonian system. Mathematical Model of water pollution will be evaluated numerically, with different input models to track environmental contamination in a water body. …”
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Unraveling the interplay of gravity and surface tension in driving waves on water’s surface by Mostafa M.A. Khater, Youbing Xia, Xiao Zhang, Raghda A.M. Attia

“…A new modern numerical technique is used to show how accurate the computational solution is, along with analytical solutions. Hamiltonian system features are also utilized to regulate the solutions’ stability. …”
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A rigorous derivation of the Hamiltonian structure for the Vlasov equation by Joseph K. Miller, Andrea R. Nahmod, Nataša Pavlović, Matthew Rosenzweig, Gigliola Staffilani

“…We consider the Vlasov equation in any spatial dimension, which has long been known [ZI76, Mor80, Gib81, MW82] to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie–Poisson type. …”
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Phase portraits and optical soliton solutions of coupled Sasa–Satsuma model in birefringent fibers by Zhao Li, Wenjie Fan, Fang Miao, Changjiang Jin

“…After that, the coupled nonlinear ordinary differential equations are transformed into two-dimensional planar dynamic system with the Hamiltonian system. According to the bifurcation theory of planar dynamical system, the phase portrait of two-dimensional dynamical system is drawn. …”
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Damping Formation Mechanism and Damping Injection of Virtual Synchronous Generator Based on Generalized Hamiltonian Theory by Yun Zeng, Jing Qian, Fengrong Yu, Hong Mei, Shige Yu

“…First, based on the energy composition and dynamic characteristics of VSG, the differential equations system of VSG is established and is transformed into the generalized Hamiltonian system. Second, the effects of the three parameters of VSG, the damping coefficient D, active power droop coefficient, and time constant of excitation <i>T_E</i> on damping characteristics are researched from a dynamic perspective, and simulation research is carried out with an isolated microgrid. …”
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Classical Hamiltonian time crystals–general theory and simple examples by Jin Dai, Antti J Niemi, Xubiao Peng

“…We focus on a Hamiltonian system with a continuous symmetry, and dynamics that takes place on a presymplectic manifold. …”
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Explicit K-Symplectic and Symplectic-like Methods for Charged Particle System in General Magnetic Field by Yulan Lu, Junbin Yuan, Haoyang Tian, Zhengwei Qin, Siyuan Chen, Hongji Zhou

“…The charged particle system can be expressed both in a canonical and a non-canonical Hamiltonian system. If the three components of the magnetic field can be integrated in closed forms, we construct explicit K-symplectic methods for the non-canonical charged particle system; otherwise, explicit symplectic-like methods can be constructed for the canonical charged particle system. …”
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Analytically and numerically, dispersive, weakly nonlinear wave packets are presented in a quasi-monochromatic medium by Mostafa M.A. Khater, Suleman H. Alfalqi, Jameel F. Alzaidi, Raghda A.M. Attia

“…To make our study more applicable, we study the stability of our solutions by focusing on the Hamiltonian system’s properties. Mathematica 13.1 checks all inputs and outcomes against the original model for further confidence.…”
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Vortices in sinusoidal shear, with applications to Jupiter by Vilasur Swaminathan, Rohith

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Explicit Runge-Kutta-Nyström methods with high order dispersion and dissipation for solving oscillatory second order ordinary differential equation by Mohamad, Munirah

“…The effects of dispersion and dissipation relations are tested on homogeneous and non-homogenous test problems which have oscillatory solutions.Derivation of symplectic explicit Runge-Kutta-Nyström method is studied for Hamiltonian system with oscillating solutions. Symplectic methods can be more efficient than non-symplectic methods for long interval of integration. …”
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Trigonometrically-fitted explicit Runge-Kutta-Nystrom methods for solving special second order ordinary differential equations with periodic solutions by Demba, Musa Ahmed

“…Meanwhile, a symplectic trigonometrically-fitted explicit RKN methods for solving Hamiltonian system with periodic solutions were derived. …”
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Vertical fit of water governing systems: A regional assessment by Peyman Arjomandi A., Seyedalireza Seyedi, Nadejda Komendantova, Ebrahim Vahdani Hulasu

“…Employing statistical mechanics methods to scrutinize Hamiltonian system costs related to administrative interactions for water supply-demand, the study assessed the structural fit of the water governance system to the basin across distinct stages: without- and with-including the ULRP. …”
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An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition by Dian Xu, Sijun Xiong, Fanxing Meng, Bo Wang, Rui Li

“…In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. …”
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Exploration of new solitons and phase characterization for the extended Gerdjikov–Ivanov equation by Tahani A. Alrebdi, Nauman Raza, Farwa Salman, Badriah Alshahrani, Abdel-Haleem Abdel-Aty, Hichem Eleuch

“…The system has been first turned into a planer dynamical system, and subsequently into a Hamiltonian system. Then the equilibrium points has been derived. …”
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An Analytical Thermal Buckling Model for Semiconductor Chips on a Substrate by Guangping Gong, Dian Xu, Sijun Xiong, Fangyu Yi, Chengbo Wang, Rui Li

“…In this paper, the thermal buckling of chips on a substrate is considered as that of plates on a Winkler elastic foundation and is studied by the symplectic superposition method (SSM) within the symplectic space-based Hamiltonian system. The solution procedure starts by converting the original problem into two subproblems, which are solved by using the separation of variables and the symplectic eigenvector expansion. …”
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Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results by Remick, Kevin, Vakakis, Alexander, McFarland, D. Michael, Quinn, D. Dane, Sapsis, Themistoklis

“…The IOM extends over finite frequency and energy ranges, consisting of a countable infinity of periodic orbits and an uncountable infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. …”
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