Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces

Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations... In this paper, we investigate a coupled system of two Korteweg-de Vries equations on a bounded domain. We discuss the long-time behavior of this system with forces on the left Dirichlet boundary conditions. We obtain that if the forces are periodic (almost periodic) with small amplitude, then the solution of the coupled system is periodic (almost periodic). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces

Chen, Mo
Mediterranean Journal of Mathematics , Volume 15 (3) – Jun 5, 2018
Download PDF
21 pages

Loading next page...
 
/lp/springer_journal/periodic-and-almost-periodic-solutions-for-a-coupled-system-of-two-0dXlfxH3fH
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
DOI
10.1007/s00009-018-1191-z
Publisher site
See Article on Publisher Site

Abstract

In this paper, we investigate a coupled system of two Korteweg-de Vries equations on a bounded domain. We discuss the long-time behavior of this system with forces on the left Dirichlet boundary conditions. We obtain that if the forces are periodic (almost periodic) with small amplitude, then the solution of the coupled system is periodic (almost periodic).

Journal

Mediterranean Journal of Mathematics – Springer Journals

Published: Jun 5, 2018

References

  • On strongly interacting internal solitary waves
    Ash, MJ; Cohen, J; Wang, G
  • Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations
    Barouna, M; Boulitea, S; Diaganab, T; Maniar, L
  • Exponential stabilization of a coupled system of Korteweg-de Vries equations with localized damping
    Bisognin, E; Bisognin, V; Perla, G
  • A model system for strong interactions between internal solitary waves
    Bona, JL; Ponce, G; Saut, JC; Tom, M
  • Forced oscillations of a damped Korteweg-de Vries equation in a quarter plane
    Bona, JL; Sun, SM; Zhang, B-Y
  • A note on the paper On the controllability of a coupled system of two Korteweg-de Vries equations
    Cerpa, E; Pazoto, AF
  • Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths
    Chu, J; Coron, J-M; Shang, P
  • Newton’s method and periodic solutions of nonlinear wave equations
    Craig, W; Wayne, CE
  • Almost periodic solution of one dimensional viscous Camassa-Holm equation
    Fu, Y; Guo, B
  • Recurrent solutions of the linearly coupled complex cubic-quintic Ginzburg-Landau equations
    Gao, P
  • Weak and strong interactions between internal solitary waves
    Gear, JA; Grimshaw, R
  • Time evolution of almost periodic solutions of the KdV equation
    Hyman, JM
  • Almost periodic solutions of the KdV equation
    Lax, PD
  • On the Cauchy problem for a coupled system of KdV equations
    Linares, F; Panthee, M
  • A coupled system of Korteweg-de Vries equation as singular limit of the Kuramoto–Sivashinsky equation
    Massarolo, CP; Menzala, GP; Pazoto, AF
  • Uniform stabilization of a coupled system of the Korteweg-de Vries equations as singular limit of the Kuramoto–Sivashinsky equations
    Massarolo, CP; Pazoto, AF
  • Stabilization of the Korteweg-de Vries equation with localized damping
    Menzala, GP; Vasconcellos, CF; Zuazua, E
  • On the controllability of a coupled system of two Korteweg-de Vries equations
    Micu, S; Ortega, JH; Pazoto, AF
  • Almost periodic solutions for a weakly dissipated hybrid system
    Micu, S; Pazoto, AF
  • On the boundedness, periodicity, and almost periodicity of solutions of some nonlinear parabolic equations
    Nakao, M
  • Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term
    Nakao, M
  • Global stabilization of a coupled system of two generalized Korteweg-de Vries type equations posed on a finite domain
    Nina, D; Pazoto, AF
  • Nonlinear stability of periodic traveling wave solutions to the Schrödinger and the modified Korteweg-de Vries equations
    Pava, JA
  • Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations
    Pava, JA; Natali, FMA
  • Uniform stabilization of a nonlinear dispersive system
    Pazoto, AF; Souza, GR
  • On the construction of almost periodic solutions for a nonlinear Schrödinger equation
    Pöschel, J
  • Periodic solutions of nonlinear hyperbolic differential equations
    Rabinowitz, PH
  • Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
    Rosier, L
  • On a model system for the oblique interaction of internal gravity waves
    Saut, JC; Tzvetkov, N
  • Forced oscillations of a class of nonlinear dispersive wave equations and their stability
    Usman, M; Zhang, B-Y
  • Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability
    Usman, M; Zhang, B-Y
  • Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
    Wayne, CE
  • Almost periodic solutions of one dimensional wave equations with periodic coefficients
    Yamaguchi, M
  • Forced oscillation of the Korteweg-de Vries–Burgers equation and its stability, Control of Nonlinear Distributed Parameter Systems (College Station, TX, 1999)
    Zhang, B-Y