On nonlinear nonlocal equations in wave theory. Part II: system of surface wave equations. Asymptotics of dissipative equations

For the system of equations for surface waves the following problems have been studied: local and global existence of solutions in time, solution breaking during finite time, smoothing of discontinuous initial perturbations in the course of time, construction of generalized solutions, and solution asymptotics for $t \to \infty$. The asymptotic behavior of solutions for $t \to \infty$ is considered for nonlinear equations with dissipation, such as the Kolmogorov-Petrovskii-Piskunov equation, the Whitham equation, the cubic Schr$\stackrel{..}{o}$dinger equation, and the Korteweg-de Vries-Burgers equation.