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8 - Conservation Laws

Published online by Cambridge University Press:  05 May 2016

Graham W. Griffiths
Affiliation:
City University London
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Chapter
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Numerical Analysis Using R
Solutions to ODEs and PDEs
, pp. 457 - 469
Publisher: Cambridge University Press
Print publication year: 2016

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References

[Abl-91] Ablowitz, M. J. and P.A., Clarkson (1991), Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society Lecture Note Series 149, Cambridge University Press.
[Dra-92] Drazin, P. G. and R. S., Johnson (1992), Solitons:An Introduction, Cambridge University Press.
[Deb-05] Debnath, L. (2005), Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhauser.
[Gar-67] Gardener, C. S., J., Greene, M., Kruskal and R. M., Miura (1967), Method for Solving the Korteweg–de Vries Equation, Physical Review Letters 19, 1095–1097.Google Scholar
[Gar-74] Gardener, C. S., J., Greene, M., Kruskal and R. M., Miura (1974), Korteweg–de Vries Equation and Generalizations. VI. Methods for Exact Solution, Communications on Pure and Applied Mathematics 27, 97–133.Google Scholar
[Gri-79] Grimshaw, R. (1979), Slowly Varying Solitary Waves. I. Korteweg–de Vries Equation, Proceedings of the Royal Society, Series A 368, 359–375.Google Scholar
[Joh-97] Johnson, R. S. (1997), A Modern Introduction to the Theory of Water Waves, Cambridge University Press.
[Jos-87] Joshi, N. (1987), Painleve Property of General Variable Coefficient Versions of the Korteweg–de Vries and Nonlinear Schrodinger Equations, Physical Letters, Series A 125, 456–460.Google Scholar
[Kad-70] Kadomtsev, B. P. and V. I., Petviashvili (1970), On the Stability of Solitary Waves in Weakly Dispersing Media, Soviet Physics–Doklady 15, 539–541.Google Scholar
[Miu-68a] Miura, R. A. (1968). Korteweg-de Vries Equation and Generalizations I.A remarkable explicit transformation. J. Math. Phys., 9, 1202-4.Google Scholar
[Miu-68b] Miura, R. A., C. S., Gardner and M. D., Kruskal (1968), Korteweg–de Vries Equation and Generalizations II. Existence of Conservation Laws and Constants of Motion, Journal of Mathematical Physics 9, 1204–1209.Google Scholar
[Sch-09] Schiesser, W. E. and G. W., Griffiths (2009), A Compendium of PartialDifferential Equation Models:Method of Lines Analysis with Matlab, Cambridge University Press.
[Zak-00] Zaki, S. I. (2000), Solitary Waves of the Korteweg–de Vries–Burgers’ Equation, Computer Physics Communications 126, 207–218.Google Scholar
[Zha-07] Zhang, D.-J. (2007), Conservation Laws and Lax Pair of Variable Coefficient KdV Equation, Chinese Physics Letters 24-1, 3021–3023.Google Scholar

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  • Conservation Laws
  • Graham W. Griffiths, City University London
  • Book: Numerical Analysis Using R
  • Online publication: 05 May 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316336069.009
Available formats
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  • Conservation Laws
  • Graham W. Griffiths, City University London
  • Book: Numerical Analysis Using R
  • Online publication: 05 May 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316336069.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Conservation Laws
  • Graham W. Griffiths, City University London
  • Book: Numerical Analysis Using R
  • Online publication: 05 May 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316336069.009
Available formats
×