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Prog. Theor. Phys. Vol. 77 No. 2 (1987) pp. 232-238

On the Prolongation Structure and Bäcklund Transformation for New Nonlinear Klein-Gorden Equations

A. Roy Chowdhury and Jayashree Mukherjee^*

International Centre for Theoretical Physics, Trieste
^*High Energy Physics Division, Department of Physics, Jadavpur University, Calcutta 700 032

(Received October 8, 1986)

Abstract:

We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual sine-Gordon and sinh-Gordon equations. The first one is of non-autonomous version of sinh-Gordon system and the second is closely related to the usual sine-Gordon theory. The first problem indicates how (x,t) dependent nonlinear equations can be treated in the prolongation theory and how a Bäcklund map can be constructed. The second one is a variation of the usual sine-Gordon equation and suggests that there may be other equations (similar to sine-Gordon) which are completely integrable. In both the cases we have been able to construct the Lax pair. We then construct an auto-Bäcklund map by following the idea of Konno and Wadati, for the generation of multisolution states.

URL : http://ptp.ipap.jp/link?PTP/77/232/
DOI : 10.1143/PTP.77.232

[ Full Text PDF : FREE ACCESS (245K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. “Nonlinear Phenomena”, Lecture Notes in Physics 189 (Springer-Verlag, Berlin, 1983).
2. A. Roy Chowdhury and T. Roy, J. Math. Phys. 21 (1980), 1416[CrossRef].
   A. Roy Chowdhury, K. Roy Chowdhury and G. Mahato, Lett. Math. Phys. 6 (1982), 423.
3. H. Q. Whalquist and F. B. Estabrook, J. Math. Phys. 16 (1975), 1[CrossRef].
4. K. Konno and M. Wadati, Prog. Theor. Phys. 53 (1975), 1652[PTP].

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