A New Generalized Heavenly Equation and the Large-Time Behavior of its Solutions

This paper studies a generalized heavenly equation, which includes the standard heavenly equation as a special case. The work starts from a vector nonlinear Riemann-Hilbert problem on the real axis. Next, the large-time asymptotic behavior for the solutions of the Cauchy problem is derived by solving the corresponding inverse Riemann-Hilbert problem. Then, by parameterizing the Riemann-Hilbert data, a class of implicit solutions is constructed.