## Solitons: An IntroductionSolitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Tranform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites are merely what is found in standard courses on mathematical physics and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to their solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks. |

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### Contents

I | 1 |

II | 7 |

III | 12 |

IV | 15 |

V | 16 |

VI | 17 |

VII | 20 |

VIII | 21 |

XLIV | 102 |

XLV | 103 |

XLVI | 106 |

XLVII | 109 |

XLVIII | 110 |

XLIX | 116 |

L | 118 |

LII | 127 |

IX | 22 |

X | 26 |

XI | 29 |

XII | 30 |

XIII | 32 |

XIV | 33 |

XV | 39 |

XVI | 40 |

XVII | 44 |

XVIII | 45 |

XIX | 48 |

XX | 56 |

XXI | 57 |

XXII | 58 |

XXIII | 60 |

XXIV | 61 |

XXV | 64 |

XXVI | 65 |

XXVII | 67 |

XXVIII | 68 |

XXIX | 70 |

XXX | 71 |

XXXI | 72 |

XXXII | 73 |

XXXIII | 74 |

XXXIV | 78 |

XXXV | 81 |

XXXVI | 83 |

XXXVII | 89 |

XXXIX | 92 |

XL | 95 |

XLI | 97 |

XLIII | 99 |

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### Common terms and phrases

6uux Ablowitz & Segur AKNS scheme amplitude arbitrary constant arbitrary function Backlund transformation becomes bilinear form bilinear operator Boussinesq equation Chap coefficients conservation laws conserved densities continuous eigenfunction continuous spectrum corresponding deduce def,ned derivatives described discrete eigenfunctions discrete eigenvalues discrete spectrum discussed dispersion relation eigenfunction Eilbeck example exists generalised give given initial profile initial-value problem integral equation interaction introduce inverse scattering transform KdV equation kink Korteweg-de Vries equation linear linearised long waves Marchenko equation matrix method Modif,ed KdV equation NLS equation nonlinear wave normalisation Note numerical obtain Painleve equation pair of equations parameter partial differential equation Phys propagation rational solution real constant satisfy scattering data sech sech2 sine-Gordon equation solitary wave solitary-wave solution soliton soliton solutions solution of equation solved Sturm-Liouville equation tanh theory two-soliton solution uxxx velocity water waves wave equation write Zabusky zero ZS scheme