Nonlinear Nonlocal Equations in the Theory of Waves

Abstract

Introduction Simplest properties of solutions of nonlinear nonlocal equations The Cauchy problem for the Whitham equation The periodic problem The system of equations of surface waves Generalized solutions The asymptotics as $t\rightarrow \infty$ of solutions of the generalized Kolmogorov-Petrovskii-Piskunov equation Asymptotics of solutions of the Whitham equation for large times Asymptotics as $t\rightarrow \infty$ of solutions of the nonlinear nonlocal Schrodinger equation Asymptotics of solutions for a system of equations of surface waves for large times The step-decaying problem for the Korteweg-de Vries-Burgers equation References.