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

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

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

Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: $u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$ where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave solutions describing one dimensional propagation of waves

Electronic structure of spinel-type LiV_2O_4

The band structure of the cubic spinel compound LiV_2O_4, which has been reported recently to show heavy Fermion behavior, has been calculated within the local-density approximation using a full-potential version of the linear augmented-plane-wave method. The results show that partially-filled V 3d bands are located about 1.9 eV above the O 2p bands and the V 3d bands are split into a lower partially-filled t_{2g} complex and an upper unoccupied e_{g} manifold. The fact that the conduction electrons originate solely from the t_{2g} bands suggests that the mechanism for the mass enhancement in this system is different from that in the 4f heavy Fermion systems, where these effects are attributed to the hybridization between the localized 4f levels and itinerant spd bands.Comment: 5 pages, revte

Modified spline-based navigation: Guaranteed safety for obstacle avoidance

© 2017, Springer International Publishing AG. Successful interactive collaboration with a human demands mobile robots to have an advanced level of autonomy, which basic requirements include social interaction, real time path planning and navigation in dynamic environment. For mobile robot path planning, potential function based methods provide classical yet powerful solutions. They are characterized with reactive local obstacle avoidance and implementation simplicity, but suffer from navigation function local minima. In this paper we propose a modification of our original spline-based path planning algorithm, which consists of two levels of planning. At the first level, Voronoi-based approach provides a number sub-optimal paths in different homotopic groups. At the second, these paths are optimized in an iterative manner with regard to selected criteria weights. A new safety criterion is integrated into both levels of path planning to guarantee path safety, while further optimization of a safe path relatively to other criteria is secondary. The modified algorithm was implemented in Matlab environment and demonstrated significant advantages over the original algorithm

Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.Comment: 19 page

The Pristine survey -- XXII. A serendipitous discovery of an extremely Li-rich very metal-poor giant and a new method of 6^6Li/7^7Li isotope measurement

We report the serendipitous discovery of a very metal-poor (VMP) Li-rich giant star ($T_{\rm eff}$ = 4690$\pm$80 K, log g = 1.34$\pm$0.13, [Fe/H] = $-2.43\pm$0.07). We analyse the Li I 6103 and 6707 \r{A} lines accounting for departures from local thermodynamic equilibrium (NLTE) and correcting for 3D effects using literature data, which yields a lithium abundance $\log\varepsilon_{Li} = 3.42\pm0.07$. Comparing lithium abundances from the two lines, in 1D NLTE we measure the isotope ratio $^6$Li/$^7$Li = 1.64$^{+1.49}_{-1.08}$ %. When correcting for 3D effects, we detect the fragile $^6$Li isotope at $2$-sigma level and the ratio $^6$Li/$^7$Li = 5.65$^{+5.05}_{-2.51}$ %. To our knowledge, this is the first $^6$Li/$^7$Li measurement in an extremely Li-rich VMP star. The Cameron-Fowler mechanism, which is proposed to produce Li-rich stars, does not imply $^6$Li production and is therefore inconsistent with our measurement when applying 3D corrections. We also derive NLTE abundances for 16 elements, most of which show similar abundances to those found in VMP stars. Sodium is an exception: [Na/Fe]$_{\rm NLTE, 1D}$ = 0.07 $\pm 0.03$, which is 0.5 dex higher than what is typical for VMP stars. This star joins the sample of rare Li-rich VMP stars, and we offer a novel way to constrain the source of lithium in such stars through isotope ratio measurements.Comment: accepted for publication in MNRA