On nonlinear nonlocal equations in wave theory. Part I: the Whitham equation

Physical problems involving nonlinear nonlocal equations (NNE) have been reviewed. The topics discussed included (i) local and global existence in time of solutions to nonlinear nonlocal equations, (ii) breaking of solutions in a finite time interval, (iii) estimation of the time of existence of solutions, (iv) smoothing of discontinuous initial perturbations with time, and (v) construction of generalized solutions.