Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent $F=1$ condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

Three-Component Soliton States in Spinor F =1 Bose-Einstein Condensates

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schr\"odinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schr\"odinger--Hirota--Maxwell--Bloch equations, along with their Lax pairs.

/pdf/integrable-2-1-dimensional-spin-models-with-self-consistent-2z6qifbzn4.pdf

Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials

In this paper, we derive a general mixed (bright-dark) multi-soliton solution to a one-dimensional multicomponent Yajima–Oikawa (YO) system, i.e., the (M + 1)-component YO system comprised of M-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients including positive, negative and mixed types. With the help of the KP-hierarchy reduction method, we firstly construct two types of general mixed N-soliton solution (two-bright–one-dark soliton and one-bright–two-dark one for SW components) to the (3+1)component YO system in detail. Then by extending the corresponding analysis to the (M + 1)-component YO system, a general mixed N-soliton solution in Gram determinant form is obtained. The expression of the mixed soliton solution also contains the general all bright and all dark N-soliton solution as special cases. Besides, the dynamical analysis shows that the inelastic collision can only take place among SW components when at least two SW components have bright solitons in mixed type soliton solution. Whereas, the dark solitons in SW components and the bright soliton in LW component always undergo usual elastic collision.

/pdf/general-mixed-multi-soliton-solutions-to-one-dimensional-26ak89utm0.pdf

General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schr\"odinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlev\'e analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright $N$-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave--short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions---(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components---result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

In this paper, we derive a general mixed (bright-dark) multi-soliton solution to a one-dimensional multicomponent Yajima-Oikawa (YO) system, i.e., the (M+1)-component YO system comprised of M-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients including positive, negative and mixed types. With the help of the KP-hierarchy reduction method, we firstly construct two types of general mixed N-soliton solution (two-bright-one-dark soliton and one-bright-two-dark one for SW components) to the (3+1)-component YO system in detail. Then by extending the corresponding analysis to the (M+1)-component YO system, a general mixed N-soliton solution in Gram determinant form is obtained. The expression of the mixed soliton solution also contains the general all bright and all dark N-soliton solution as special cases. Besides, the dynamical analysis shows that the inelastic collision can only take place among SW components when at least two SW components have bright solitons in mixed type soliton solution. Whereas, the dark solitons in SW components and the bright soliton in LW component always undergo usual elastic collision.

It is shown that many sublattice isotropic XY chain with magnon-phonon interactions at the long-wave approximations may be described by generalized Zakharov's system with U(p, q) isogroup. Two-sublattice XY chain through the Jordan-Wigner transformations reduced to Su-Schriffer-Heeger coupled electron-phonon model in the quasi-one-dimensional conductor polyacetylene (CH)x theory. The Hamiltonian structure of U(p, q) Zakharov's system and its "ultrarelativistic" limit (i.e., the Yajima-Oikawa system with U(p, q) isogroup) are studied. The linear problem and the generating functionals for infinite series of additional integrals of motion for U(p, q) Yajima-Oikawa system are constructed. Four types of soliton solutions under different boundary conditions and appropriate integrals of particles number and energy are found. The quasistationary and ultra-relativistic limits are discussed.

https://iopscience.iop.org/article/10.1088/0031-8949/33/4/013/pdf

Particle-Like Excitations in Many Component Magnon-Phonon Systems

The decay of zero area pulses is investigated for the Korteweg-de Vries equation. By using a linear representation of the Korteweg-de Vries equation the problem is reduced to the solution of a simple quantum-mechanical problem. The transcendent equation for eigenvalues is obtained and its numerical analysis is carried out. The region of existence of the discrete energy levels, corresponding to a soliton lattice of the Korteweg-de Vries equation, is found. The existence of a threshold of discrete energy levels in the zero area potential is established. The numerical simulation results on the decay of zero area pulses are compared with those predicted for the discrete energy levels.

Kh T Kholmurodov

Papers

Particle-Like Excitations in Many Component Magnon-Phonon Systems

Threshold of KDV solitons production