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. |
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Περιεχόμενα
I | 1 |
II | 7 |
III | 12 |
IV | 15 |
V | 16 |
VI | 17 |
VII | 20 |
IX | 21 |
XLV | 102 |
XLVI | 103 |
XLVII | 106 |
XLVIII | 109 |
XLIX | 110 |
L | 116 |
LI | 118 |
LII | 127 |
X | 22 |
XI | 26 |
XII | 29 |
XIII | 30 |
XIV | 32 |
XV | 33 |
XVI | 39 |
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XVIII | 44 |
XIX | 45 |
XX | 48 |
XXI | 56 |
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XXIII | 58 |
XXIV | 60 |
XXV | 61 |
XXVI | 64 |
XXVIII | 65 |
XXIX | 67 |
XXX | 68 |
XXXI | 70 |
XXXII | 71 |
XXXIII | 72 |
XXXIV | 73 |
XXXV | 74 |
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XXXIX | 89 |
XLI | 92 |
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LIII | 128 |
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LXXX | 196 |
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amplitude applications arbitrary constant associated assume asymptotic Bäcklund transformation becomes behaviour bilinear called Chap chapter choice choose clear coefficients complete consider constant continuous convenient corresponding defined depend derivatives described determined differential equation discrete eigenvalues discussed dispersion eigenfunction evolution equations examine example exercise exists expressed Finally fixed follows function Further give given Hence initial integral interaction introduce KDV equation linear matrix method nonlinear Note numerical obtain operator Painlevé pair parameter partial particular periodic positive potential problem propagation properties relation represented requires respectively satisfies scattering problem scheme sech shown similar simple sine-Gordon equation solitary wave solitary-wave solution soliton solution solved spectrum theory transformation turn usually Uxxx write written yield zero дх