Abstract
In this paper, the hodograph equivalent short pulse equations are investigated via the Darboux transformation, we derive the soliton and positon solutions from the “seed” solution, and then, the decomposition of the lower-order positons into single-solitons is given analytically when time T is sufficiently large. As a notable new result, we obtain the exploding soliton and positon solutions of the sine-Gordon equation from the hodograph equivalent short pulse equations.
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