Article
Mathematics, Applied
Benjamin Dodson
Summary: This paper generalizes a weak sequential result from Fan (2021) to non scattering solutions in dimensions equal to or greater than 2. No symmetry assumptions are necessary for the initial data, building upon Dodson's (2020) previous result in one dimension.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Optics
E. Tchomgo Felenou
Summary: We examine the feasibility of analyzing the behavior of a radiating pulse during its propagation in an optical fiber transmission line using the collective coordinates approach. The dynamics of the radiation waves can be described well by variational equations. We find that these waves do not maintain a constant profile during propagation but continuously spread out. The frequency of the radiation remains constant and can be compared to the carrying frequency in the GHz to THz range. Precise knowledge of the frequency or temporal position of the radiation allows for the possibility of removing the radiation in one operation through spectral or temporal filtering.
Article
Mathematics, Applied
Christopher C. Hogan, Jason Murphy
Summary: We investigate the dynamics of an accelerated soliton in the cubic nonlinear Schrödinger equation with an external potential. We find that for sufficiently large velocities, the soliton can effectively transmit through the potential. This result extends previous studies on delta potentials with or without linear bound states.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Xin Wang, Jiao Wei
Summary: The study investigates the space-shifted nonlocal PT symmetric nonlinear Schrodinger equation, constructing three types of Darboux transformations based on the symmetry conditions of the linear matrix spectral problem. Various analytical solutions such as periodic, breather-like and bounded soliton solutions are derived from three kinds of spectral configurations, showing the dynamics of these solutions to the space-shifted nonlocal PT symmetric NLS equation.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Engineering, Mechanical
Jianping Wu
Summary: This paper proposes a reduction approach for solving the shifted nonlocal nonlinear Schrödinger equation by imposing constraints on the general solution of the AKNS(q,r) system. The approach has the advantages of being purely algebraic and applicable to other shifted nonlocal NLS equations.
NONLINEAR DYNAMICS
(2022)
Article
Chemistry, Physical
Subarna Sasmal, Martin McCullagh, Glen M. Hocky
Summary: In this work, we show that applying Linear Discriminant Analysis (LDA) to atomic positions is an effective way to obtain a good reaction coordinate between two different states of a biomolecule. The lack of rotational and translational invariance has prevented the use of atomic coordinates in enhanced sampling studies. However, by considering molecular configurations as members of equivalence classes in size-and-shape space, we overcome this issue and produce reaction coordinates that effectively characterize the transition between two states and allow for free energy estimation using enhanced sampling MD techniques.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Engineering, Mechanical
Jianping Wu
Summary: A new general nonlocal reverse-space nonlinear Schrodinger equation is proposed by imposing a nonlocal reverse-space symmetry constraint on a general coupled NLS equation. The equation is physically meaningful and can be used to obtain corresponding solutions of the general coupled NLS equation with special initial conditions. A novel Riemann-Hilbert method is developed to solve the proposed nonlocal equation, and soliton solutions are rigorously obtained by solving the RH problem with the complicated spectral symmetry structure. Some new soliton dynamical behaviors underlying the soliton solutions are also theoretically investigated and graphically simulated.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
Summary: In this paper, we study the one-dimensional nonlinear Schro center dot dinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation has a one-parameter family of solitary wave solutions in both the focusing and defocusing cases. We establish the asymptotic stability for solitary wave solutions satisfying a suitable spectral condition, which requires that the linearized operator around the solitary wave has a two-dimensional generalized kernel and no other eigenvalues or resonances. Our results extend previous ones beyond the regime of small solitary waves and also extend the results of [19, 29] from orbital stability to asymptotic stability for a suitable family of solitary waves.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2023)
Article
Materials Science, Multidisciplinary
Joel Bruno Gonpe Tafo, Fabien Kenmogne, Alexandre Mando Kongne, Roger Eno, David Yemele
Summary: In this study, the propagation of modulated solitons in a 2D nonlinear reaction diffusion electrical network is investigated. The circuit elements in both the propagation and transverse directions act as nonlinear resistances. Model equations for the circuit are derived and simplified to the 2D nonlinear dissipative Schrodinger equation, which governs the propagation of small dissipative amplitude signals in the network. The solutions of this equation are 2D dissipative pulse and dark solitons, whose amplitude narrows as time increases, depending on the sign of the product of dispersive and nonlinearity coefficients. The analytical analysis is confirmed by numerical simulations.
RESULTS IN PHYSICS
(2023)
Article
Chemistry, Physical
Line Mouaffac, Karen Palacio-Rodriguez, Fabio Pietrucci
Summary: This paper presents an algorithm that addresses the challenges of finding optimal reaction coordinates and predicting accurate kinetic rates through a Monte Carlo approach. The algorithm generates a sequence of reaction coordinates from a limited number of reactive molecular dynamics trajectories, progressively reducing the kinetic rate. The method is benchmarked on an analytic double-well system and applied to complex atomistic systems, demonstrating its feasibility and accuracy.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Engineering, Mechanical
Yan Li, Jian Li, Ruiqi Wang
Summary: In this paper, soliton solutions for the nonlocal Kundu-nonlinear Schrodinger equation were studied using the Darboux transformation. The N-soliton solutions for the equation were investigated through the one-fold and n-fold Darboux transformation. Exact solutions for the equation with different spectral parameters were obtained and corresponding graphs were provided.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Bo Wei, Jing Liang
Summary: Multiple dark and antidark soliton solutions for a space shifted PT symmetric nonlocal nonlinear Schrodinger equation are constructed and classified using the Kadomtsev-Petviashvili hierarchy reduction method and Hirota's bilinear technique. The amplitude values and collision coordinates of two-soliton solutions are discussed theoretically and numerically, and the parameter conditions of these solutions are given. Furthermore, the four-soliton solutions show a superposition of two two-soliton solutions, indicating that higher-order soliton solutions should have similar properties.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Jun Yang, Hai-Fang Song, Miao-Shuang Fang, Li-Yuan Ma
Summary: This paper focuses on the explicit analytic solutions for the focusing and defocusing space shifted nonlocal nonlinear Schrodinger equation. The authors obtained the nonsingular N-soliton solutions for the defocusing case and constructed multirogue wave solutions for the focusing case using Darboux transformation. The dynamic behaviors of the solutions were studied theoretically and numerically, and it was found that the space shift parameter reveals more general dynamic characteristics in the space shifted nonlocal NLS equation.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Jun Yang, Miao-Shuang Fang, Lin Luo, Li-Yuan Ma
Summary: This paper investigates a generalized integrable discrete nonlinear Schrodinger equation, analyzing the Darboux transformation and soliton solutions. It demonstrates that the integrable properties of the generalized discrete NLS equation lead to their continuous counterparts as the discrete space step approaches zero.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Fluids & Plasmas
Giacomo Roberti, Gennady El, Alexander Tovbis, Francois Copie, Pierre Suret, Stephane Randoux
Summary: In this study, a breather gas for the focusing nonlinear Schrodinger equation is numerically realized by constructing a random ensemble of approximately 50 similar breathers through the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized as elementary quasiparticles of the respective gases, and the interaction properties of the constructed breather gases are investigated by comparing the mean propagation velocity with predictions of spectral kinetic theory.
Article
Astronomy & Astrophysics
Yves Brihaye, Adolfo Cisterna, Betti Hartmann, Gabriel Luchini
Article
Physics, Particles & Fields
C. P. Constantinidis, L. A. Ferreira, G. Luchini
JOURNAL OF HIGH ENERGY PHYSICS
(2015)
Article
Physics, Particles & Fields
H. E. Baron, W. J. Zakrzewski
JOURNAL OF HIGH ENERGY PHYSICS
(2016)
Article
Physics, Particles & Fields
L. A. Ferreira, G. Luchini
Article
Astronomy & Astrophysics
L. A. Ferreira, G. Luchini
Article
Physics, Particles & Fields
L. A. Ferreira, G. Luchini, Wojtek J. Zakrzewski
JOURNAL OF HIGH ENERGY PHYSICS
(2012)
Article
Physics, Multidisciplinary
C. P. Constantinidis, L. A. Ferreira, G. Luchini
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2019)
Article
Environmental Sciences
Robyn Horan, R. Gowri, Pawan S. Wable, Helen Baron, Virginie D. J. Keller, Kaushal K. Garg, Pradeep P. Mujumdar, Helen Houghton-Carr, Gwyn Rees
Summary: This study compared the predictive capability of three hydrological models and their mean ensemble in a heavily influenced catchment in Peninsular India. The results showed that the mean ensemble had better predictive ability in catchments with reservoirs, indicating that utilizing multiple models could help overcome uncertainties in input data and poor reservoir operation functionality within individual models.
Article
Environmental Sciences
Robyn Horan, Nathan J. Rickards, Alexandra Kaelin, Helen E. Baron, Thomas Thomas, Virginie D. J. Keller, Prabhas K. Mishra, Manish K. Nema, Sekhar Muddu, Kaushal K. Garg, Rishi Pathak, Helen A. Houghton-Carr, Harry Dixon, Sharad K. Jain, Gwyn Rees
Summary: The study demonstrates the success of improving model performance by enhancing groundwater and reservoir routines in the GWAVA model, allowing for better traceability of simulated water balance components without significantly increasing model complexity and data requirements.
Article
Physics, Multidisciplinary
Gabriel Luchini, Victor B. Zache
Summary: This study demonstrates that the laws of electromagnetism in (D + 1)-dimensional Minkowski space-time M, specifically for D = 1, 2, and 3, can be derived from the integral representation of the zero-curvature equation in the corresponding loop space L(D-1)(M). The conservation of electric charge is attributed to a hidden symmetry in this representation of the dynamical equations.
BRAZILIAN JOURNAL OF PHYSICS
(2022)
Article
Green & Sustainable Science & Technology
Robyn. Horan, Pawan S. Wable, Veena Srinivasan, Helen E. Baron, Virginie J. D. Keller, Kaushal K. Garg, Nathan Rickards, Mike Simpson, Helen A. Houghton-Carr, H. Gwyn Rees
Summary: The study focuses on the impact of small-scale water storage interventions in the Cauvery Basin of India, finding that farm bunds have a negligible effect while tanks and check dams have a more significant impact on water balance. The open water surface of the interventions leads to increased evaporation losses, while the change in simulated groundwater storage is not as significant as expected. The model adaptation used in this study advances the understanding of small-scale storage interventions in large-scale hydrological models.
Article
Astronomy & Astrophysics
C. P. Constantinidis, L. A. Ferreira, G. Luchini
Proceedings Paper
Physics, Applied
Luiz. A. Ferreira, G. Luchini, Wojtek J. Zakrzewski
NONLINEAR AND MODERN MATHEMATICAL PHYSICS
(2013)
