## Selected Papers of Morikazu TodaThis volume contains selected papers of Dr Morikazu Toda. The papers are arranged in chronological order of publishing dates. Among Dr Toda's many contributions, his works on liquids and nonlinear lattice dynamics should be mentioned. The one-dimensional lattice where nearest neighboring particles interact through an exponential potential is called the Toda lattice which is a miracle and indeed a jewel in theoretical physics. The papers in this volume can be grouped into five subjects: statistical mechanics, theory of liquids and solutions, lattice dynamics, Toda lattice and soliton theory and its applications. |

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### Contents

Reprinted papers | 1 |

On the Virial Theorem | 7 |

Notes on the Theory of High Polymer Solutions with A Ishikara | 31 |

C Hsiung | 32 |

On the Relation between Fermions and Bosons | 42 |

On the Theory of Quantum Liquids I Surface Tension and Stress | 48 |

Diffusion in Velocity Space and T nsport Phenomena | 54 |

Localized Vibration and Random Walk with T Kotera and Y Kogure | 61 |

The Criterion for the Existence of a Gap in the Optical Band | 139 |

A Solitoii and Two Solitoiis in an Exponential Lattice | 161 |

J Phys Soc Japan 39 1975 11961203 | 176 |

Lecture Notes | 219 |

Chopping Phenomenon of a Nonlinear System | 220 |

Problems in Nonlinear Dynamics | 234 |

Solitons and Heat Conduction | 247 |

Experiment on SolitonImpurity Interaction in Nonlinear Lattice | 261 |

Statistical Dynamics of Systems of Interacting Oscillators | 69 |

Some Properties of the Pair Distribution Function | 84 |

OneDimensional Dual Transformation | 90 |

Wave Propagation in Auharmonic Lattices | 103 |

Coupled Nonlinear Waves | 280 |

Partition Function of Nonlinear Lattice | 293 |

List of Misprints | 313 |

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### Common terms and phrases

anharmonicity approximation assume asymptotic atoms Backlund transformation boundary condition Boussinesq equation calculation canonical transformation chain coefficient collision consider continuum limit cosh denotes density derived displacement dual equation of motion exponential lattice expression Fermi gas Fermi surface finite force constant formula frequency given by Eq Hamiltonian harmonic Hirota incident soliton infinite integral isotope Japan KdV equation Kompeito Korteweg-de Vries equation Kruskal LC circuit linear liquid localized mode localized vibration mass impurity mass ratio Math matrix method mixed crystal modulus molecules momentum Morikazu nonlinear lattice normal modes obtain optical band oscillator partition function phase shift Phys Physics polymers potential energy problem Prog propagation pulse quantum reflected wave relation result shown sinh soliton soliton amplitude solution spring statistical mechanics Suppl surface tension temperature theory thermal tion Toda lattice University of Education velocity virial theorem WADATI wave function wave length wave train Zabusky