## Symmetries and Integrability of Difference EquationsPeter A. Clarkson, Frank W. Nijhoff There has in recent years been a remarkable growth of interest in the area of discrete integrable systems. Much progress has been made by applying symmetry groups to the study of differential equations, and connections have been made to other topics such as numerical methods, cellular automata and mathematical physics. This volume comprises state of the art articles from almost all the leading workers in this important and rapidly developing area, making it a necessary resource for all researchers interested in discrete integrable systems or related subjects. |

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### Contents

IV | 3 |

V | 15 |

VIII | 23 |

X | 41 |

XI | 43 |

XIII | 56 |

XV | 64 |

XVII | 79 |

XLII | 245 |

XLIII | 247 |

XLV | 261 |

XLVII | 275 |

XLIX | 285 |

L | 287 |

LII | 299 |

LIII | 311 |

XIX | 95 |

XX | 97 |

XXII | 109 |

XXIV | 122 |

XXV | 137 |

XXVII | 151 |

XXIX | 165 |

XXXIII | 178 |

XXXVI | 195 |

XXXVII | 197 |

XXXVIII | 206 |

XL | 217 |

XLI | 228 |

LIV | 313 |

LVI | 325 |

LVIII | 334 |

LIX | 343 |

LX | 345 |

LXI | 353 |

LXII | 370 |

LXIII | 385 |

LXV | 387 |

LXVII | 402 |

LXX | 410 |

LXXII | 420 |

### Common terms and phrases

2DTL Ablowitz analysis applications arbitrary asymptotics Bäcklund transformation canonical cellular automata classical coefficients compute consider constant construct continuous continuum limit coordinates corresponding Darboux Darboux transformation defined denote derived difference equations differential equations differential-difference dimensional discrete analogue discrete equation discrete isothermic surfaces discrete Painlevé equations discrete version discrete zero curvature equa evolution equations example finite Fokas geometry given Grammaticos Hamiltonian heat equation Hirota homogeneous spaces hyperelliptic integrable discretization integrable systems invariant isospectral lattice hierarchy Lax operators Lax pair Lett Lie algebra linear linearisable Macdonald polynomials Math Mathematics matrix models method nonisospectral nonlinear obtained orthogonal polynomials Painlevé equations parameter Phys preprint properties q-exponential quantum Ramani rational solutions relations Riccati equation satisfy Schrödinger soliton solve spectral problem Springer structure symplectic map theorem theory tions ultra-discrete University of Kent variables vector fields Winternitz zero curvature equation

### References to this book

Difference Equations, Special Functions and Orthogonal Polynomials ... Saber Elaydi Limited preview - 2007 |