Prog. Theor. Phys. Vol. 75 No. 5 (1986) pp. 1250-1253
On the Inverse Problem and Bäcklund Transformation for the Nonlinear Equation uxxx-(3/2)α2u2ux+3∂x-1utt-3αux∂x-1ut=0
High Energy Physics Division, Department of Physics, Jadavpur University, Calcutta-700 032
(Received September 10, 1985)
We have considered the integrability of a nonlinear equation of the form: uxxx-(3/2)α2u2ux+3∂x-1utt-3αux∂x-1ut=0 which is midway between the Boussinesq and its modified form. Our approach is that of prolongation structure, through which we have constructed the matrix representation of the Lax pair. We have found a generalized Bäcklund transformation connecting two solutions of the same equation. Lastly we comment on the connection of our equation with the modified K-P equation in three dimensions.
DOI : 10.1143/PTP.75.1250
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