Other
Scientific paper
May 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cqgra...5..743g&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 5, May 1, 1988, p. 743-765.
Other
11
Cosmology, Gravitational Fields, Newton Theory, Solitary Waves, Astronomical Models, Asymptotic Methods, Galactic Evolution, Magnetohydrodynamics
Scientific paper
It is shown that the plane-wave solutions for the equations governing the motion of a self-gravitating isothermal fluid in Newtonian hydrodynamics are generated by a sine-Gordon equation which is solvable by an 'inverse scattering' transformation. A transformation procedure is outlined by means of which one can construct solutions of the gravity system out of a pair of solutions of the sine-Gordon equation which are interrelated via an auto-Baecklund transformation. In general the solutions to the gravity system are obtained in a parametric representation in terms of characteristic coordinates. All solutions of the gravity system generated by the one-soliton and two-soliton solutions of the sine-Gordon equation can be constructed explicitly. These might provide models for the evolution of flat structures as they are predicted to arise in the process of galaxy formation.
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