Abstract
After the Lamb substitution the 2D sine-Gordon equation was solved. Three classes of solutions for this equation were found. Ad hoc the 2D sine-Gordon equation was reduced to an algebraic system consisting of three equations. The solutions given of the 2D sine-Gordon equation are a generalization of the solutions of the 1D sine-Gordon equation. They are also a generalization of the solutions of the equation phi xx+yy=sin phi (x,y).
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