Dispersion equations and a comparison of different quasi-periodic solutions of the sine-Gordon equation

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Abstract
A system of dispersion equations for quasi-periodic solutions of the multidimensional sine-Gordon equation is discussed. This system of algebraical equations determines the parameters appearing in the solution which involves abstract theta-functions. In the case of the two-phase quasi-periodic solutions, it is shown that the form involving theta-functions represents a broader class than the class of solutions given by the expression 4 tan-1 fg. The condition for the equivalence of both classes is also reported.