A direct method for solving the generalized sine-Gordon equation II

The generalized sine-Gordon (sG) equation $u_{tx}=(1+\nu\partial_x^2)\sin\,u$ was derived as an integrable generalization of the sG equation. In a previous paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is referred to as I, we developed a systematic method for solving the generalized sG equation with $\nu=-1$. Here, we address the equation with $\nu=1$. By solving the equation analytically, we find that the structure of solutions differs substantially from that of the former equation. In particular, we show that the equation exhibits kink and breather solutions and does not admit multi-valued solutions like loop solitons as obtained in I. We also demonstrate that the equation reduces to the short pulse and sG equations in appropriate scaling limits. The limiting forms of the multisoliton solutions are also presented. Last, we provide a recipe for deriving an infinite number of conservation laws by using a novel B\"acklund transformation connecting solutions of the sG and generalized sG equations.Comment: To appear in J. Phys. A: Math. Theor. The first part of this paper has been published in J. Phys. A: Math. Theor. 43 (2010) 10520

Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation

In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different parametric regimes and (ii) a loop soliton with a conventional soliton in detail.Comment: Published in Physica Scripta (2012

Chemical potential shift in La(1-x)Sr(x)MnO(3): Photoemission test of the phase separation scenario

We have studied the chemical potential shift in La(1-x)Sr(x)MnO(3) as a function of doped hole concentration by core-level x-ray photoemission. The shift is monotonous, which means that there is no electronic phase separation on a macroscopic scale, whereas it is consistent with the nano-meter scale cluster formation induced by chemical disorder. Comparison of the observed shift with the shift deduced from the electronic specific heat indicates that hole doping in La(1-x)Sr(x)MnO(3) is well described by the rigid-band picture. In particular no mass enhancement toward the metal-insulator boundary was implied by the chemical potential shift, consistent with the electronic specific heat data.Comment: 7 pages, 3 figures, to be published in Europhysics Letter

Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model

Collective field theory for Calogero model represents particles with fractional statistics in terms of hydrodynamic modes -- density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field -- quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.Comment: 5 pages, 1 figur

On the origin of heavy quasiparticles in LiV_2O_4

An explanation is provided for the heavy quasiparticle excitations in LiV_2O_4. It differs considerably from that of other known heavy-fermion systems. Main ingredients of our theory are the cubic spinel structure of the material and strong short-range correlations of the d electrons. The large gamma-coefficient is shown to result from excitations of Heisenberg spin 1/2 rings and chains. The required coupling constant is calculated from LDA+U calculations and is found to be of the right size. Also the calculated Sommerfeld-Wilson ratio is reasonably close to the observed one.Comment: REVTEX, 5 pages, 2 figure

Modulation theory of quantum tunneling into a Calogero-Sutherland fluid

Quantum hydrodynamics of interacting electrons with a parabolic single particle spectrum is studied using the Calogero-Sutherland model. The effective action and modulation equations, describing evolution of periodic excitations in the fluid, are derived. Applications to the problem of a single electron tunneling into the FQHE edge state are discussed

On the tau-functions of the Degasperis-Procesi equation

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be publishe

Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

Electronic states and magnetic excitations in LiV2O4: Exact diagonalization study

Motivated by recent inelastic neutron scattering experiment we examine magnetic properties of LiV2O4. We consider a model which describes the half-filled localized A1g spins interacting via frustrated antiferromagnetic Heisenberg exchange and coupled by local Hund's interaction with the 1/8-filled itinerant Eg band, and study it within an exact diagonalization scheme. In the present study we limited the analysis to the case of the cluster of two isolated tetrahedrons. We obtained that both the ground state structure and low-lying excitations depend strongly on the value of the Hund's coupling which favors the triplet states. With increasing temperature the triplet states become more and more populated which results in the formation of non-zero residual magnetic moment. We present the temperature dependence of calculated magnetic moment and of the spin-spin correlation functions at different values of Hund's coupling and compare them with the experimental results.Comment: 7 pages. 6 eps figure