Jun Mada et al 2008 J. Phys. A: Math. Theor. 41 175207 doi:10.1088/1751-8113/41/17/175207
The box–ball system and the N-soliton solution of the ultradiscrete KdV equation
Jun Mada1, Makoto Idzumi2 and Tetsuji Tokihiro1
Show affiliationsAny state of the box–ball system (BBS) together with its time evolution is described by the N-soliton solution (with appropriate choice of N) of the ultradiscrete KdV equation. It is shown that simultaneous elimination of all '10'-walls in a state of the BBS corresponds exactly to reducing the parameters that determine 'the size of a soliton' by one. This observation leads to an expression for the solution to the initial-value problem (IVP) for the BBS. Expressions for the solution to the IVP for the ultradiscrete Toda molecule equation and the periodic BBS are also presented.
- PACS
- MSC
- Subjects
- Dates
-
Issue 17 (2 May 2008)
Received 8 February 2008
Published 15 April 2008
-
The box–ball system and the N-soliton solution of the ultradiscrete KdV equation
Jun Mada et al 2008 J. Phys. A: Math. Theor. 41 175207
-
Size effects in statistical fracture
Mikko J Alava et al 2009 J. Phys. D: Appl. Phys. 42 214012
-
Parylene-based electret power generators
Hsi-wen Lo and Yu-Chong Tai 2008 J. Micromech. Microeng. 18 104006
-
Separability and entanglement of quantum states based on covariance matrices
Ming Li et al 2008 J. Phys. A: Math. Theor. 41 202002
-
The role of spin state on the local atomic and electronic structures of some metalloporphyrin complexes
S A Suchkova et al 2009 J. Phys.: Conf. Ser. 190 012211
-
Reproducible dynamic dark ring lattices for ultracold atoms
N Houston et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 211001
-
Simulating ITER plasma startup and rampdown scenarios in the DIII-D tokamak
G.L. Jackson et al 2009 Nucl. Fusion 49 115027
-
Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam
G P Berman et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 225403
-
Capillary waves' dynamics at the nanoscale
Rafael Delgado-Buscalioni et al 2008 J. Phys.: Condens. Matter 20 494229
-
Estimation of Weibull parameters from parameters of initial distribution of flaw size
C Wakabayashi et al 2009 J. Phys.: Conf. Ser. 191 012006
Users also read
What's this?- One-dimensional anyons with competing δ-function and derivative δ-function potentials
- Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies
- q-difference equations of KdV type and Chazy-type second-degree difference equations
-symmetric models of scatteringRelated review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
-
Notes on Yang–Mills–Higgs monopoles and dyons on
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities
- Quantum integrability and functional equations: applications to the spectral problem of AdS/CFT and two-dimensional sigma models