Related papers: Dark solitons of the Gross-Neveu model
The Gross-Neveu model in 1+1 dimensions is generalized to the case of different scalar and pseudoscalar coupling constants. This enables us to interpolate smoothly between the standard massless Gross-Neveu models with either discrete or…
An explicit two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one…
A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations, motivated to reconsider solutions to the nonlinear Schr\"odinger (NLS) equation on two half-lines connected via…
We obtain a bilocal classical field theory as the large $N$ limit of the chiral Gross--Neveu (or non--abelian Thirring) model. Exact classical solutions that describe topological solitons are obtained. It is shown that their mass spectrum…
For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann-Hilbert…
In this paper, local and nonlocal complex reduction of a discrete and a semi-discrete negative order Ablowitz-Kaup-Newell- Segur equations is studied. Cauchy matrix type solutions, including soliton solutions and Jordan-block solutions, for…
In a previous paper (Matsuno 2011 {\it J. Phys. A: Math. Theore.} {\bf 44} 495202), we have presented a determinantal expression of the bright $N$-soliton solution for a multi-component modified nonlinear Schr\"odinger (NLS) system with…
We consider certain boundary conditions supporting soliton solutions in the generalized non-linear Schr\"{o}dinger equation (AKNS). Using the dressing transformation (DT) method and the related tau functions we study the AKNS$_{r}$ system…
We present a simple approach for finding $N$-soliton solution and the corresponding Jost solutions of the derivative nonlinear Scr\"{o}dinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse…
In a previous study (Matsuno Y, J. Phys. A: Math. Theor. 45(2012)23202), we have developed a systematic method for obtaining the bright soliton solutions of the Fokas-Lenells derivative nonlinear Schr\"odinger equation (FL equation shortly)…
A direct method is developed for constructing the bright $N$-soliton solution of a multi-component modified nonlinear Schr\"odinger equation. Specifically, the two different expressions of the solution are obtained both of which are…
Baryons in the large N limit of (1+1)-dimensional Gross-Neveu models with either discrete or continuous chiral symmetry have long been known. We generalize their construction to the case where the symmetry is explicitly broken by a bare…
We study dark soliton solutions of a multi-component Gross--Pitaevskii equation for hyperfine spin F=1 spinor Bose--Einstein condensate. The interactions are supposed to be inter-atomic repulsive and anti-ferromagnetic ones of equal…
This paper studies the quantum lattice Boltzmann scheme for the nonlinear Dirac equations for Gross-Neveu model in $1+1$ dimensions. The initial data for the scheme are assumed to be convergent in $L^2$. Then for any $T\ge 0$ the…
We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions…
We derive a set of bilinear identities for the determinants of the matrices that have been used to construct the dark soliton solutions for various models. To give examples of the application of the obtained identities we present soliton…
Soliton solutions of non-linear NLS and KdV equations are related to compatibility condition between matrices M and H describing the movement of an auxilary function Psi in the x,t plane with a zero curvature condition. Non-linear equation…
The Degasperis-Procesi (DP) equation \begin{align} &u_t-u_{txx}+3\kappa u_x+4uu_x=3u_x u_{xx}+uu_{xxx}, \nonumber \end{align} serving as a model delineating the propagation of shallow water waves, stands as a completely integrable system…
We derive and discuss the complete set of exact solutions to the one-dimensional Bogoliubov-de Gennes equations for small amplitude excitations around general grey soliton solutions to the cubic nonlinear Schr\"odinger equation. Our results…
We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as $N$ tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like…