Solitons, ubiquitous in nonlinear sciences, are wavepackets which maintain their characteristic shape upon propagation. In optics, they have been observed and extensively studied in optical fibers. The spontaneous generation of a dissipative Kerr soliton (DKS) train in an optical microresonator pumped with continuous wave (CW) coherent light has placed solitons at the heart of optical frequency comb research in recent years. The commonly observed soliton has a ``sech-shaped envelope resulting from resonator cubic nonlinearity balanced by its quadratic anomalous group velocity dispersion (GVD). Here we exploit the Lagrangian variational method to show that CW pumping of a Kerr microresonator featuring quartic GVD forms a pure quartic soliton (PQS) with Gaussian envelope. We find analytical expressions for pulse parameters in terms of experimentally relevant quantities and derive an area theorem. Predictions of the analytical calculations are validated with extensive numerical simulations. The broader bandwidth and flatter spectral envelope of a PQS, compared to a DKS of the same pulse width and peak power, make it superior for applications requiring small line-to-line power variation in frequency comb harmonics.
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