Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

We report discovery of collinear-magnetism-driven ferroelectricity in the Ising chain magnet Ca3Co2-xMn(x)O6 (x approximately 0.96). Neutron diffraction shows that Co2+ and Mn4+ ions alternating along the chains exhibit an up-up-down-down ( upward arrow upward arrow downward arrow downward arrow) magnetic order. The ferroelectricity results from the inversion symmetry breaking in the upward arrow upward arrow downward arrow downward arrow spin chain with an alternating charge order. Unlike in spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in Ca3(Co,Mn)2O6 occurs through exchange striction associated with symmetric superexchange.

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Ferroelectricity in an Ising Chain Magnet

Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations

Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas

Optical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger system

Electron-positron-ion plasmas are found in the primordial Universe, active galactic nuclei, surroundings of black holes and peripheries of neutron stars. We focus our attention on a modified Zakharov-Kuznetsov (mZK) equation which describes the ion acoustic drift solitary waves in an electron-positron-ion magnetoplasma. Lie symmetry generators and groups are presented by virtue of the Lie symmetry method. Optimal system of the one-dimensional subalgebras is presented, which is influenced via the ratio of the unperturbed ion density to electron density nio/neo, the ratio of the unperturbed positron density to electron density npo/neo, the ratio of the electron temperature to positron temperature Te/Tp and the normalized ion drift velocity v o * . Based on the optimal system, we construct the power-series, multi-soliton, breather-like and periodic-wave solutions. Two types of the elastic interactions, including the overtaking and head-on interactions between (among) two (three) solitons are discussed. We find that the amplitudes of the solitons and periodic waves are positively related to the electron Debye length λDe and negatively related to |ρi| with ρi as the ion Larmor radius. Besides, we find that the mZK equation is not only strictly self-adjoint but also nonlinearly self-adjoint. Condition for the nonlinear self-adjointness is related to nio/neo, npo/neo, Te/Tp and v o * . Based on the nonlinear self-adjointness of the mZK equation, conservation laws, which are related to nio/neo, npo/neo, Te/Tp, v o * , λDe, ρi and may be associated with the conservation of momentum and energy, are obtained.

Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma

Under investigation is a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a fluid. Via the Hirota method and symbolic computation, we obtain the mixed lump-kink and mixed rogue wave-kink solutions. Through the mixed lump-kink solutions, we observe three different phenomena between a lump and one kink. For the fusion phenomenon, a lump and a kink are merged with the lump’s energy transferring into the kink gradually, until the lump merges into the kink completely. Fission phenomenon displays that a lump separates from a kink. The last phenomenon shows that a lump travels together with a kink with their amplitudes unchanged. In addition, we graphically study the interaction between a rogue wave and a pair of the kinks. It can be observed that the rogue wave arises from one kink and disappears into the other kink. At certain time, the amplitude of the rogue wave reaches the maximum.

Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics

Solitons for the (2+1)-dimensional Konopelchenko–Dubrovsky equations

Optical fiber communication system is one of the core supporting systems of the modern internet age. In this paper, under investigation is a higher-order nonlinear Schrodinger system for the simultaneous propagation of two ultrashort optical pulses in an optical fiber. Based on the Lax pair, with respect to the two-component electric fields, infinitely-many conservation laws and one/N-fold binary Darboux transformations are derived, where N = 2 , 3 , … . Solitons are discussed: (1) Nondegenerate one dark–dark soliton, which is black or gray in each component, is obtained. ϵ has no relation with the soliton amplitude in each component, but has a linear correlation with the soliton velocities, where ϵ, σ1 and σ2 are the constant coefficients in the system; (2) Overtaking and head-on interactions between the two dark–dark solitons as well as the bound state are depicted. With the decreasing value of σ1, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes decrease. With the decreasing value of σ2, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes do not change; (3) Interaction among the three overtaking solitons and interaction between a bound state and one soliton are displayed. We find that the interactions between the two solitons and among the three solitons are elastic.

Conservation laws, binary Darboux transformations and solitons for a higher-order nonlinear Schrödinger system

A set of the coherently-coupled nonlinear Schrodinger equations with the positive coherent coupling terms, which are related to the optical fiber communication, are studied through the binary Darboux transformation with the dimensional reduction. Formalisms of the solutions appear as the mixtures of the polynomial functions with exponential functions. When the spectral parameter is real, we obtain different kinds of the solutions, such as the soliton, degenerate-soliton, periodic, and soliton-like rational solutions. When the spectral parameter is complex with a non-zero imaginary part, we obtain the rogue waves and twisted rogue-wave pairs, and show that an eye-shaped rogue wave splits into a twisted rogue-wave pair.

Yu-Qiang Yuan

Papers

Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma

Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics

Solitons for the (2+1)-dimensional Konopelchenko–Dubrovsky equations

Conservation laws, binary Darboux transformations and solitons for a higher-order nonlinear Schrödinger system

Rogue waves and solitons of the coherently-coupled nonlinear Schrödinger equations with the positive coherent coupling