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The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the…

Statistical Mechanics · Physics 2017-12-27 Armen Poghosyan , Nickolay Izmailian , Ralph Kenna

We consider the Schroedinger equation with a subcritical focusing power nonlinearity on a noncompact metric graph, and prove that for every finite edge there exists a threshold value of the mass, beyond which there exists a positive bound…

Analysis of PDEs · Mathematics 2017-06-26 Riccardo Adami , Enrico Serra , Paolo Tilli

Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of…

Quantum Physics · Physics 2008-11-26 R. Parwani , G. Tabia

A trapping region is a compact set that is forward invariant with respect to the dynamics. Existence of a trapping region certifies boundedness of trajectories, and the size of the set provides an estimate of the ultimate bound. Prior work…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Diganta Bhattacharjee , Shih-Chi Liao , Peter J. Seiler , Maziar S. Hemati

Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…

Dynamical Systems · Mathematics 2026-04-06 Y. T. Feng

Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…

Statistical Mechanics · Physics 2026-03-04 Ruicheng Bao , Shiling Liang

We examine some new DNLS-like equations that arise when considering strongly-coupled electron-vibration systems, where the local oscillator potential is anharmonic. In particular, we focus on a single, rather general nonlinear vibrational…

Disordered Systems and Neural Networks · Physics 2009-11-07 M. I. Molina

It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…

Other Condensed Matter · Physics 2008-01-24 F. Kh. Abdullaev , Yu. V. Bludov , S. V. Dmitriev , P. G. Kevrekidis , V. V. Konotop

We examine a fractional version of the discrete Nonlinear Schr\"{o}dinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor…

Pattern Formation and Solitons · Physics 2019-11-04 M. I. Molina

We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the Discrete Nonlinear Schr\"odinger Equation (DNLS). In the…

Pattern Formation and Solitons · Physics 2016-03-30 H. Hennig , T. Neff , R. Fleischmann

We extend earlier work [Phys.Rev.Lett. 84, 3740 (2000)] on the statistical mechanics of the cubic one-dimensional discrete nonlinear Schrodinger (DNLS) equation to a more general class of models, including higher dimensionalities and…

Statistical Mechanics · Physics 2007-05-23 Magnus Johansson , Kim O. Rasmussen

We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative stiffness). In such a system with constant…

Classical Physics · Physics 2019-05-07 S. N. Gavrilov , E. V. Shishkina , Yu. A. Mochalova

The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a…

Robotics · Computer Science 2022-02-18 Wanda Zhao , Alexandr Klimchik , Anatol Pashkevich , Damien Chablat

For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…

Pattern Formation and Solitons · Physics 2022-01-05 Faustino Palmero , Mario I. Molina , Jesús Cuevas-Maraver , Panayotis G. Kevrekidis

We study localization, pinning, and mobility in the fractional discrete nonlinear Schr\"odinger equation (fDNLS) with generalized power-law coupling. A finite-dimensional spatial-dynamics reduction of the nonlocal recurrence yields onsite…

Classical Analysis and ODEs · Mathematics 2025-09-12 Brian Choi , Austin Marstaller , Alejandro Aceves

We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be…

We discuss the stability properties of the solutions of the general nonlinear Schroedinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time (PT) symmetric superpotential $W(x)$ that we considered…

Pattern Formation and Solitons · Physics 2016-12-21 Fred Cooper , Avinash Khare , Andrew Comech , Bogdan Mihaila , John F. Dawson , Avadh Saxena

We prove that that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as constraint can be obtained in the $\Gamma$-limit of the…

Analysis of PDEs · Mathematics 2022-06-29 Stefan Krömer , Philipp Reiter

We study the statistical mechanics of the one-dimensional discrete nonlinear Schr\"odinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the…

Pattern Formation and Solitons · Physics 2013-04-23 Mogens R. Samuelsen , Avinash Khare , Avadh Saxena , Kim Ø. Rasmussen

The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The…

Condensed Matter · Physics 2009-10-28 B. C. Gupta , K. Kundu