Two-dimensional soliton cellular automaton of deautonomized Toda-type

A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.Comment: 11 pages, LaTeX fil

Continuous vacua in bilinear soliton equations

We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by A(D_{\vec x})\bd GF=0,\, B(D_{\vec x})(\bd FF - \bd GG)=0 where both $A$ and $B$ are even polynomials in their variables, then there can be a continuum of vacua, parametrized by a vacuum angle $\phi$. The ramifications of this freedom on the construction of one- and two-soliton solutions are discussed. We find, e.g., that once the angle $\phi$ is fixed and we choose $u=\arctan G/F$ as the physical quantity, then there are four different solitons (or kinks) connecting the vacuum angles $\pm\phi$, $\pm\phi\pm\Pi2$ (defined modulo $\pi$). The most interesting result is the existence of a ``ghost'' soliton; it goes over to the vacuum in isolation, but interacts with ``normal'' solitons by giving them a finite phase shift.Comment: 9 pages in Latex + 3 figures (not included

M\"obius Symmetry of Discrete Time Soliton Equations

We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various $q$-difference soliton equations by reductions.Comment: 21 pages, 4 figure, epsfig.st

Entangled coherent states: teleportation and decoherence

When a superposition $(|\alpha>-|-\alpha>)$ of two coherent states with opposite phase falls upon a 50-50 beamsplitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of $\alpha$, as was recently discovered by O. Hirota and M. Sasaki. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat statesComment: 11 pages LaTeX, 3 eps figures. Submitted to Phys. Rev.

Toda Lattice and Tomimatsu-Sato Solutions

We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions completely and for generic cases partially.Comment: LaTeX 8 page

A Characterization of Discrete Time Soliton Equations

We propose a method to characterize discrete time evolution equations, which generalize discrete time soliton equations, including the $q$-difference Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.Comment: 13 page

Solutions of a discretized Toda field equation for DrD_{r} from Analytic Bethe Ansatz

Commuting transfer matrices of $U_{q}(X_{r}^{(1)})$ vertex models obey the functional relations which can be viewed as an $X_{r}$ type Toda field equation on discrete space time. Based on analytic Bethe ansatz we present, for $X_{r}=D_{r}$, a new expression of its solution in terms of determinants and Pfaffians.Comment: Latex, 14 pages, ioplppt.sty and iopl12.sty assume

Multiple addition theorem for discrete and continuous nonlinear problems

The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the factorization of N-tuple product of the shifted functions and it seems to be useful for analysis of soliton type continuous and discrete processes in the N+1 space-time. A close relation with the natural generalization of bi- and tri-linear operators into multiple linear operators concludes the paper.Comment: 9 page