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A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

Numerical Analysis · Mathematics 2011-06-07 Miquel Grau-Sánchez , José Luis Díaz-Barrero

Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the $\ell_1$-regularized version to the sparsity constrained models. This paper is carried out…

Optimization and Control · Mathematics 2021-11-23 Rui Wang , Naihua Xiu , Shenglong Zhou

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave…

Optics · Physics 2018-04-11 Pengfei Li , Dumitru Mihalache , Boris A. Malomed

We consider the Schrodinger equation with a logarithmic nonlinearity and a repulsive harmonic potential. Depending on the parameters of the equation, the solution may or may not be dispersive. When dispersion occurs, it does with an…

Numerical Analysis · Mathematics 2023-12-04 Remi Carles , Chunmei Su

We apply the method of modulation equations to numerically solve the NLS with multichannel dynamics, given by a trapped localized state and radiation. This approach employs the modulation theory of Soffer-Weinstein, which gives a system of…

High Energy Physics - Theory · Physics 2015-06-19 Avy Soffer , Xiaofei Zhao

We present a quantum computational framework that systematically converts classical linear iterative algorithms with fixed iteration operators into their quantum counterparts using the Schr\"odingerization technique [Shi Jin, Nana Liu and…

Numerical Analysis · Mathematics 2025-05-13 Shi Jin , Nana Liu , Chuwen Ma , Yue Yu

We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of…

Analysis of PDEs · Mathematics 2015-05-13 Hans Christianson , Jeremy Marzuola

We suggest the method of derivation of Hamilton equations which describe the motion of solitons along non-uniform and time dependent large-scale background in case of wave dynamics described by the completely integrable equations in the…

Pattern Formation and Solitons · Physics 2024-07-08 A. M. Kamchatnov

We derive a straightforward variational method to construct embedded soliton solutions of the third-order nonlinear Sch\"odinger equation and analytically demonstrate that these solitons exist as a continuous family. We argue that a…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Debabrata Pal , Sk. Golam Ali , B. Talukdar

This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about…

Numerical Analysis · Mathematics 2021-10-08 Eisa Khosravi Dehdezi , Saeed Karimi

The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its…

Exactly Solvable and Integrable Systems · Physics 2017-04-19 Xiao-Yong Wen , Zhenya Yan , Yunqing Yang

The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…

Pattern Formation and Solitons · Physics 2025-09-15 Pedro Fittipaldi de Castro , Wladimir Alejandro Benalcazar

We introduce a versatile platform for studying nonlinear out-of-equilibrium physics. The platform is based on a slow light setup where an optical waveguide is interfaced with cold atoms to realize the driven nonlinear Schr\"odinger equation…

Quantum Physics · Physics 2015-03-20 Priyam Das , Changsuk Noh , Dimitris G. Angelakis

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…

Computational Engineering, Finance, and Science · Computer Science 2024-09-21 W. Chen

We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse non locality. Making a convenient reference to a widely used material -nematic liquid crystals-, we derive a new form of the discrete…

Pattern Formation and Solitons · Physics 2009-11-11 Andrea Fratalocchi , Gaetano Assanto

We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…

Numerical Analysis · Mathematics 2018-09-21 Dmytro Sytnyk

The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…

Numerical Analysis · Mathematics 2024-04-25 A. Torres-Hernandez , F. Brambila-Paz , P. M. Rodrigo , E. De-la-Vega , C. C. Calabrese

The Onsager-Stefan-Maxwell (OSM) equations are an important model of mass transport in multicomponent flows with multiple chemical species. They describe the coupling of diffusive fluxes between species, accounting for their interactions…

Numerical Analysis · Mathematics 2026-04-22 Kars Knook , Aaron Baier-Reinio , Patrick E. Farrell

A previously unknown bright N-soliton solution for an intermediate nonlinear Schr\"{o}dinger equation of focusing type is presented. This equation is constructed as a reduction of an integrable system related to a Sato equation of a…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Yohei Tutiya

A method for approximating dark soliton solutions of the nonlinear Schrodinger equation under the influence of perturbations is presented. The problem is broken into an inner region, where core of the soliton resides, and an outer region,…

Mathematical Physics · Physics 2015-05-19 Mark J. Ablowitz , Sean D. Nixon , Theodoros P. Horikis , Dimitri J. Frantzeskakis