Solitons: An IntroductionCambridge University Press, 9 Φεβ 1989 - 226 σελίδες Solitons: 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. |
Περιεχόμενα
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 |
LIII | 128 |
LIV | 131 |
LV | 137 |
LVI | 140 |
LVII | 142 |
LVIII | 143 |
LIX | 144 |
LX | 146 |
LXI | 149 |
LXIII | 151 |
LXIV | 152 |
LXV | 154 |
LXVI | 157 |
LXVII | 162 |
169 | |
LXX | 171 |
LXXI | 172 |
LXXII | 174 |
LXXIII | 177 |
LXXIV | 180 |
LXXV | 182 |
LXXVI | 183 |
LXXVII | 184 |
LXXVIII | 186 |
LXXIX | 187 |
LXXXII | 190 |
LXXXV | 196 |
LXXXVI | 201 |
LXXXVII | 205 |
LXXXVIII | 213 |
LXXXIX | 220 |
221 | |
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Συχνά εμφανιζόμενοι όροι και φράσεις
AKNS scheme 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 Eilbeck example generalised give given Hence initial profile 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 Schrödinger equation nonlinear wave normalisation Note numerical obtain operator Painlevé equation parameter Phys potential propagation rational solution 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 Uxxx v₁ velocity w₁ w₂ water waves wave equation zero ZS scheme биих дх Иххх