The (3+1)-dimensional dispersionless integrable hierarchy and nonlinear Riemann-Hilbert problem associated with the Doubrov-Ferapontov modified heavenly equation

Abstract

According to the classification of integrable complex Monge-Ampere equations by Doubrov and Ferapontov, the modified heavenly equation is a typical (3+1)-dimensional dispersionless and canonical integrable equation.In this paper we use the eigenfunctions of the Doubrov-Ferapontov modified heavenly equation to obtain a related hierarchy. Next we construct the Lax-Sato equations with Hamiltonian vector fields and Zakharov-Shabat type equations which are equivalent to the hierarchy. The nonlinear Riemann-Hilbert problem is also applied to study the solution of Doubrov-Ferapontov modified heavenly equation.