Related papers: New types of two component NLS-type equations
We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the presence of $k-$local interactions decaying as $\sim 1/r^\alpha$ with distance $r$. Two…
Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…
A special class of multicomponent NLS equations, generalizing the vector NLS and related to the {\bf BD.I}-type symmetric are shown to be integrable through the inverse scattering method (ISM). The corresponding fundamental analytic…
Some modified (defocusing) non-linear Schr\"odinger models (MNLS) possess infinite towers of anomalous conservation laws with asymptotically conserved charges. The so-called anomalies of the quasi-conservation laws vanish upon space-time…
We consider the cubic nonlinear Schr\"odinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the knowledge that the NLS is an effective equation for a system…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
Using complex notation, we present new simple expressions for two pairs of complex supercharges in HKT supersymmetric sigma models. The second pair of supercharges depends on the holomorphic antisymmetric "hypercomplex structure" tensor…
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems…
We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these equations and obtain soliton solutions. We find all possible local and nonlocal reductions…
We write the integral formula of Tarasov-Varchenko type for the solutions to the quantum Knizhnik-Zamolodchikov associated with a tensor product the of vector representations of sl_n. We consider the case where the deformation parameter q…
The soliton solution of the integrable coupled nonlinear Schrodinger equation (NLS) of Manakov type is investigated by using Zakharov-Shabat (ZS) scheme. We get the bright N-solitons solution by solving the integrable uncoupled NLS of…
We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schr\"odinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order…
The general multi-soliton solution of the integrable coupled nonlinear Schrodinger equation (NLS) of Manakov type is investigated by using Zakharov-Shabat (ZS) scheme. We get the bright and dark multi-soliton solution using inverse…
Soliton interactions in systems modelled by coupled nonlinear Schroedinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features : shape changing…
Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization…
In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu-Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known…
Treating an integrable quad-equation along with its two generalised symmetries as a compatible system allows one to construct an auto-B\"acklund transformation for solutions of the related NLS-type system. A fixed periodic reduction of the…
We discuss extension of soliton theory and integrable systems to noncommutative spaces, focusing on integrable aspects of noncommutative anti-self-dual Yang-Mills equations. We give wide class of exact solutions by solving a Riemann-Hilbert…
We compute the order alpha_s^3 (next-to-leading) corrections to the Wilson coefficients of the Delta F=2 effective Hamiltonian in the Minimal Supersymmetric Standard Model with completely arbitrary soft terms. These results are relevant for…
Here, a class of nonlinear moving boundary problems for a novel extension of a two-component mKdV system is shown to admit exact solution via application of a hybrid Ermakov-Ray-Reid / Painlev\'e II symmetry ansatz.The mKdV system has its…