English
Related papers

Related papers: Dark solitons of the Gross-Neveu model

200 papers

This work is devoted to systematically study general $N$-soliton solutions possibly containing multiple degenerate soliton groups (DSGs), in the context of the sharp-line Maxwell-Bloch equations with a zero background.We also show that…

Exactly Solvable and Integrable Systems · Physics 2025-01-28 Sitai Li

We derive a bound on the energy of the general (p,q)-supersymmetric two-dimensional massive sigma model with torsion, in terms of the topological and Noether charges that appear as central charges in its supersymmetry algebra.The bound is…

High Energy Physics - Theory · Physics 2016-09-06 G. Papadopoulos , P. K. Townsend

This paper studies a class of nonlinear Dirac equations with cubic terms in $R^{1+1}$, which include the equations for the massive Thirring model and the massive Gross-Neveu model. Under the assumption that the initial data has bounded…

Analysis of PDEs · Mathematics 2014-07-17 Yongqian Zhang , Qin Zhao

This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schr\"odinger equation. Crucially, we present analytic expressions for the four linearly-independent zero eigenvalue solutions (also known as…

Quantum Gases · Physics 2015-05-27 Andrew Sykes

We report exact bright and dark soliton solution to the nonlinear evolution equation derived by Moses and Wise [Phys. Rev. Lett. 97, 073903, (2006)] for cascaded quadratic media beyond the slowly varying envelope approximations. The…

Optics · Physics 2012-12-18 Amarendra K. Sarma , Anjan Biswas

For the nonlocal Davey-Stewartson I equation, the Darboux transformation is considered and explicit expressions of the solutions are obtained. Like the nonlocal equations in 1+1 dimensions, many solutions may have singularities. However, by…

Exactly Solvable and Integrable Systems · Physics 2018-08-09 Zi-Xiang Zhou

N-dark-dark solitons in the generally coupled integrable NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed.…

Pattern Formation and Solitons · Physics 2010-11-12 Yasuhiro Ohta , Dengshan Wang , Jianke Yang

We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG) in $\mathbb{R}^{1+d}$, $d\ge1$, which behave as a soliton or a sum of solitons in large time. In the spirit of other articles focusing on the supercritical…

Analysis of PDEs · Mathematics 2021-06-18 Xavier Friederich

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 V. S. Shchesnovich , J. Yang

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not holds in real…

Pattern Formation and Solitons · Physics 2022-08-12 N. Mao , L. -C. Zhao

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

We rigorously establish the existence of dark-bright solitons as traveling wave solutions to a one dimensional defocusing Gross-Pitaevskii system, a widely used model for describing mixtures of Bose-Einstein condensates and nonlinear…

Analysis of PDEs · Mathematics 2026-02-13 Salvador López-Martínez

We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and…

High Energy Physics - Theory · Physics 2020-04-22 Emin Nugaev , Andrey Shkerin

We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Vivek M Vyas , T Soloman Raju , C Nagaraja Kumar , Prasanta K Panigrahi

We characterize the soliton solutions and their interactions for a system of coupled evolution equations of nonlinear Schr\"odinger (NLS) type that models the dynamics in one-dimensional repulsive Bose-Einstein condensates with spin one,…

Quantum Gases · Physics 2021-04-22 Asela Abeya , Barbara Prinari , Gino Biondini , P. G. Kevrekidis

In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions.…

Exactly Solvable and Integrable Systems · Physics 2011-05-27 Jarmo Hietarinta , Da-jun Zhang

We construct smooth non-supersymmetric soliton solutions with D1-brane, D5-brane and momentum charges in type IIB supergravity compactified on T^4 x S^1, with the charges along the compact directions. This generalises previous studies of…

High Energy Physics - Theory · Physics 2009-11-11 Vishnu Jejjala , Owen Madden , Simon F. Ross , Georgina Titchener

We analyze soliton solutions in the duality-based matrix model. There are two types of solution, a one soliton-antisoliton solution (with the constant boundary condition at infinity) and a periodic solution with an infinite number of…

High Energy Physics - Theory · Physics 2007-05-23 V. Bardek , S. Meljanac

The determinant formula for N-soliton solutions of the Bullough-Dodd-Jiber-Shabat equation on a finite-gap background is obtained. Nonsingularity conditions for them and their asymptotics are investigated.

Mathematical Physics · Physics 2015-06-26 I. Yu. Cherdantzev , R. A. Sharipov

In this article, we focus on investigating the focusing Kundu-Eckhaus equation with nonzero boundary condition. A appropriate two-sheeted Riemann surface is introduced to map the spectral parameter $k$ into a single-valued parameter $z$.…

Exactly Solvable and Integrable Systems · Physics 2020-12-02 Lili Wen , Engui Fan