Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation

The large-time behaviour of solutions of the Cauchy problem for the modified Kawahara equation {u(t) - partial derivative(x)u(3) - a/3 partial derivative(3)(x)u + b/5 partial derivative(5)(x)u = 0, (t, x) is an element of R-2, u(0, x) - u(0)(x), x is an element of R, where a, b > 0, is investigated. Under the assumptions that the total mass of the initial data integral u(0)( x) dx is nonzero and the initial data u(0) are small in the norm of H-2,H-1 it is proved that a global-in-time solution exists and estimates for its large-time decay are found. Bibliography: 19 titles.