Type: Article

Self-similar asymptotics for solutions to the intermediate long-wave equation

Bernal-Vilchis, Fernando; Naumkin, PI;

Abstract:

We consider the Cauchy problem for the intermediate long-wave equation u(t) - partial derivative(x) u(2) + 1/vu(x) + V P integral(R) 1/2v coth(pi (y - x)/2v u(yy) (t, y) dy = 0, where v > 0. Our purpose in this paper is to prove the large time asymptotic behavior of solutions under the nonzero mass condition integral u(0) (x) dx not equal 0.