Particle-Like Excitations in Many Component Magnon-Phonon Systems
TL;DR: In this paper, it was 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.
Abstract: 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.
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TL;DR: It is experimentally demonstrated the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F=1 condensate and theoretical analysis shows that small-amplitudesolitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems.
Abstract: 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.
98 citations
TL;DR: This paper identifies 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, and deduces the equivalent nonlinear Schrodinger family of equations.
Abstract: 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.
65 citations
TL;DR: In this article, a general mixed (bright-dark) multi-soliton solution to a one-dimensional multicomponent Yajima-Oikawa (YO) system was derived.
Abstract: 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.
43 citations
TL;DR: The three-soliton interaction is explored and the pairwise nature of collisions is demonstrated and the fascinating state restoration property is unraveled.
Abstract: 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.
38 citations
TL;DR: In this paper, a general mixed (bright-dark) multi-soliton solution to a one-dimensional multicomponent Yajima-Oikawa (YO) system was derived.
Abstract: 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.
38 citations
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TL;DR: In this paper, the authors present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion.
Abstract: We present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion. The results provide an explanation of the mobile neutral defect observed in undoped ${(\mathrm{CH})}_{x}$. Since the soliton formation energy is less than that needed to create band excitation, solitons play a fundamental role in the charge-transfer doping mechanism.
4,562 citations
IBM1
TL;DR: In this article, two genuinely quantum models for an antiferromagnetic linear chain with nearest neighbor interactions are constructed and solved exactly, in the sense that the ground state, all the elementary excitations and the free energy are found.
3,382 citations
TL;DR: A theoretical analysis of the excitation spectrum of long-chain polyenes is presented in this paper, where one electronic state is localized at the gap center for each soliton or antisoliton present and the soliton's energy of formation, length, mass, activation energy for motion, and electronic properties are calculated.
Abstract: A theoretical analysis of the excitation spectrum of long-chain polyenes is presented. Because of the twofold degeneracy of the ground state of the dimerized chain, elementary excitations corresponding to topological solitons are obtained. The solitons can have three charge states $Q=0$. $\ifmmode\pm\else\textpm\fi{}e$. The neutral soliton has spin one-half while the charged solitons have spin zero. One electronic state is localized at the gap center for each soliton or antisoliton present. The soliton's energy of formation, length, mass, activation energy for motion, and electronic properties are calculated. These results are compared with experiment.
2,276 citations
TL;DR: A survey of the properties of soliton-type solutions to non-linear wave equations appearing in various fields of physics is given in this paper, where the results of computer experiments on the dynamics of the formation and interaction (in one-space-dimensional geometry) of solit-type objects are presented at length.
499 citations
01 Sep 1981
TL;DR: In this article, a transmission rate of ≃1 Tbits/sec (≃0.1 T bits/s) per 30 km can be achieved using envelope solitons with peak power of approximately 10 W in a monomode optical fiber, respectively.
Abstract: A transmission rate of ≃1 Tbits/sec (≃0.1 Tbits/s) per 30 km can be achieved using envelope solitons with peak power of ≃10 W (≃10 mW) in a monomode optical fiber, respectively. Unlike the linear pulse in which the bit rate is limited by the group dispersion, the bit rate of soliton transmission is limited by the fiber loss and the input power. Conditions for achieving optimum transmission rate using solitons are theoretically obtained including the effects of fiber loss and second order group dispersion.
326 citations