By Frank B. Estabrook (auth.), Rodolfo Martini (eds.)

ISBN-10: 3540100180

ISBN-13: 9783540100188

ISBN-10: 354038166X

ISBN-13: 9783540381662

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Extra info for Geometrical Approaches to Differential Equations: Proceedings of the Fourth Scheveningen Conference on Differential Equations, The Netherlands August 26 – 31, 1979

Sample text

T. 9xt = transformations. and local EVP and that these compatibility are prime candidates The Backlund has the same general for the sine-Gordon (with the F's, of Again KdV (in this case) would be conditions for study. transformation, form as EVP and ISF. 14b) w h e r e ~ is a real parameter. 13). 13). 's arise in soliton theory. T. 14a,b) conditions is an extra feature. 11) (with coefficient +12 rather than -6 - this is x x a simple scale change). 15) a first order system for w' is manifest. The compatibility conditions are, of course, 27 the potential KdV equation.

18, 1658 (1977). 21. F. Lund, Phys. Rev. Lett. 38, 1175 (1977) and Phys. Rev. DI5, 1540 (1977). 22. A. Sym and J. Corones, Phys. Rev. Lett. 42, 1099 (1979). 23. M. Lakshmanan, Phys. Lett. 61A, 53 (1977), and 64A, 353 (1978). 24. M. Crampin, Phys. Lett. 66A, 243 (1978). 25. M. Crampin, F. Pirani and D. Robinson, Lett. Math. Phys. 2, 15 (1977). ON B~CKLUND 2 + I AND TRANSFORmaTIONS AND 3 + I - DIMENSIONAL SOLUTIONS SINE - GORDON TO THE EQUATION P L Christiansen L a b o r a t o r y of A p p l i e d M a t h e m a t i c a l P h y s i c s T h e T e c h n i c a l U n i v e r s i t y of D e n m a r k DK-2800 Abstract.

It is, unfortunately However, discussed far from clear that all BT's can be arrived at in this way. again the question deserves study particularly in the previous lecture. role that nonlinear To summarize, In any event, this example shows the important actions of groups can play in soliton theory. , bilocally. some interesting in light of BT's of the four interpretations In the next lecture we will show how to give to these objects. 39 IV. A Brief Comment on Geometry and Solitons In closing I will note some geometric aspects of soliton theory that are natural in the context of the last two lectures.

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Geometrical Approaches to Differential Equations: Proceedings of the Fourth Scheveningen Conference on Differential Equations, The Netherlands August 26 – 31, 1979 by Frank B. Estabrook (auth.), Rodolfo Martini (eds.)


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