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Amplitude analysis and branching fraction measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>
We report an amplitude analysis and branching fraction measurement of ${D}_{s}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decay using a data sample of $3.19\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded with BESIII detector at a center-of-mass energy of 4.178 GeV. We perform a model-independent partial wave analysis in the low ${K}^{+}{K}^{\ensuremath{-}}$ mass region to determine the ${K}^{+}{K}^{\ensuremath{-}}$ S-wave line …