  This work introduces a new class of Runge-Kutta methods for solving
nonlinearly partitioned initial value problems. These new methods, named
nonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and
component-partitioned Runge-Kutta methods, and allow one to distribute
different types of implicitness within nonlinear terms. The paper introduces
the NPRK framework and discusses order conditions, linear stability, and the
derivation of implicit-explicit and implicit-implicit NPRK integrators. The
paper concludes with numerical experiments that demonstrate the utility of NPRK
methods for solving viscous Burger's and the gray thermal radiation transport
equations.
