Bell and Kink type, Weierstrass and Jacobi elliptic, multiwave, kinky breather, M-shaped and periodic-kink-cross rational solutions for Einstein's vacuum field model.

This article uses appropriate transformations and the sub-ODE method to reveal multiwave, homoclinic breather, M-shaped rational, periodic cross rational, kink cross rational, periodic cross kink, and other soliton solutions for Einstein's vacuum field problem. Additionally, the interaction of rational solitons in the M shape with an exponential function and a double exponential form is disclosed. [ABSTRACT FROM AUTHOR]