On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks (Q2832442)

The authors investigate the generalized dispersionless Kadomtsev-Petviashvili equation NEWLINE\[NEWLINE (u_t+u^mu_x)_x+\sum_{i=1}^{n-1}\partial_{y_i}^2 u=0, NEWLINE\]NEWLINE where \(m,n\in\mathbb{N}\). Using the invariance of this equation under motions on the paraboloid, the authors construct the family of exact solutions. These solutions are then used to study the long-time behavior of solutions to the Cauchy problem with small and localized initial data and to describe the wave breaking phenomenon.