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We investigate the small but finite amplitude solitary Kinetic Alfv\'{e}nwaves (KAWs) in low $\beta$ plasmas with superthermal electrons modeled by akappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equationdescribing the evolution of KAWs is derived by using the standard reductiveperturbation method. Examining the dependence of the nonlinear and dispersioncoefficients of the KdV equation on the superthermal parameter $\kappa$, plasma$\beta$ and obliqueness of propagation, we show that these parameters maychange substantially the shape and size of solitary KAW pulses. Onlysub-Alfv\'enic, compressive solitons are supported. We then extend the study toexamine kinetic Alfv\'en rogue waves by deriving a nonlinear Schr\"{o}dingerequation from {the KdV} equation. Rational solutions that form rogue waveenvelopes are obtained. We examine how the behavior of rogue waves depends onthe plasma parameters in question, finding that the rogue envelopes are loweredwith increasing electron superthermality whereas the opposite is true when theplasma $\beta$ increases. The findings of this study may find applications tolow $\beta$ plasmas in astrophysical environments where particles aresuperthermally distributed.

Kinetic Alfv\'{e}n solitary and rogue waves in superthermal plasmas