Exact String Solutions and the Open String - D-Brane System in Non-Constant Background Fields I

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New exact string solutions in non-constant background fields are found and it is shown that some of them are compatible with the boundary conditions for the open string - D-brane system. Extension of the constraint algebra is proposed and discussed.
LaTeX, 10 pages, no figures; V2: minor improvements in the text, references rewritten, report-no added

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