Related papers: Algebraic solitons in the massive Thirring model
An algebraic soliton of the massive Thirring model (MTM) is expressed by the simplest rational solution of the MTM with the spatial decay of $\mathcal{O}(x^{-1})$. The corresponding potential is related to a simple embedded eigenvalue in…
The newly discovered exponential and algebraic double-soliton solutions of the massive Thirring model in laboratory coordinates are placed in the context of the inverse scattering transform. We show that the exponential double-solitons…
We study the global dynamics of the collision of two solitons having the same mass for one-dimensional Nonlinear Schr\"odinger models with multi-power nonlinearity. For any natural number k, it is verified that if the incoming speed v…
Families of solutions to the field equations of the covariant BRST invariant effective action of the membrane theory are constructed. The equations are discussed in a double dimensional reduction, they lead to a nonlinear equation for a one…
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…
Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the coupled massive Thirring and the coupled Soler model to…
In this article, we investigate monotonicity of limit wave speed of periodic traveling wave solutions for a perturbed generalized KdV equation via Abelian integral. We have answered an open problem outlined by Yan et al. (2014) and the…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
The potential of the $A_2$ quantum elliptic model (3-body Calogero-Moser elliptic model) is defined by the pairwise three-body interaction through Weierstrass $\wp$-function and has a single coupling constant. A change of variables has been…
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…
The nonlinear Schroedinger equation with a third-order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this…
Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multi-wave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero…
Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a linear equation coupled to the Korteweg-de Vries equation. The…
We show that an interacting double soliton solution to the perturbed mKdV equation is close in $H^2$ to a double soliton following an effective dynamics obtained as Hamilton's equations for the restriction of the mKdV Hamiltonian to the…
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…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…
In linear science, the wave motion equation with general D'Alembert wave solutions is one of the fundamental models. The D'Alembert wave is an arbitrary travelling wave moving along one direction under a fixed model (material) dependent…
The precise modeling of binary black hole coalescences in generic planar orbits is a crucial step to disentangle dynamical and isolated binary formation channels through gravitational-wave observations. The merger regime of such…
We present a large family of {\it{exact}} solitary wave solutions of the one dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain/loss, in both expulsive and regular parabolic confinement regimes. The…
The soliton dressing matrices for the higher-order zeros of the Riemann-Hilbert problem for the $N$-wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric…