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. |
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
amplitude arbitrary constant asymptotic Bäcklund transformation behaviour bilinear form bilinear operator Chap coefficients conservation laws continuous spectrum corresponding defined derivatives described discrete eigenfunctions discrete eigenvalues discrete spectrum discussed eigenfunction eikx Eilbeck example f₁ generalised given Hence initial profile initial-value problem integral equation interaction introduce inverse scattering transform k₁ KdV equation Korteweg-de Vries equation linear linearised Marchenko equation matrix method modified KdV equation N-soliton NLS equation nonlinear evolution equations nonlinear Schrödinger equation nonlinear wave normalisation Note numerical obtain operator Painlevé equation parameter Phys potential propagation real constant satisfies scattering data sech sech² sine-Gordon equation solitary wave solitary-wave solution soliton solutions solution of equation solved Sturm-Liouville equation tanh theory two-soliton solution u₁ Uxxx w₁ water waves wave equation zero ZS scheme λε дх