Advances in Differential Equations

Periodic problem for a model nonlinear evolution equation

Elena I. Kaikina, Pavel I. Naumkin, and Ilya A. Shishmarev

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We study the large time asymptotic behavior of solutions to the periodic problem for a model nonlinear evolution equation. This equation has a general structure, it contains many well-known equations of mathematical physics, such as: the Korteweg-de Vries equation and nonlinear Schrödinger equation. We find the asymptotic representation of solution. Depending on the linear part of equation and the structure of the nonlinearity the solution can exponentially decay with time, oscillate or grow exponentially with time. Taking into account the symmetry of the nonlinear term we consider the case of large initial data.

Article information

Adv. Differential Equations Volume 7, Number 5 (2002), 581-616.

First available in Project Euclid: 27 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 35B10: Periodic solutions 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]


Kaikina, Elena I.; Naumkin, Pavel I.; Shishmarev, Ilya A. Periodic problem for a model nonlinear evolution equation. Adv. Differential Equations 7 (2002), no. 5, 581--616.

Export citation