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Closed-form expressions for integrals of MKdV and sine-Gordon maps
We present closed-form expressions for approximately N integrals of 2N -dimensional maps. The maps are obtained by travelling wave reductions of the modified Korteweg–de Vries equation and of the sine-Gordon equation, respectively. We provide the integrating factors corresponding to the integrals. Moreover we show how the integrals and the integrating factors relate to the staircase method.