Generalized dispersive equations of higher orders posed on bounded intervals: local theory

Abstract

Initial-boundary value problems for nonlinear dispersive equations of evolution of order $2l+1,l\in \mathbb{N}$ with a convective term of the form $u^k{u}_x,k\in \mathbb{N}$ have been considered on intervals $(0,L),L\in (0,+\infty )$. The existence and uniqueness of local regular solutions have been established.