Chaos for a damped and forced KdV equation

DOI10.1016/j.physd.2004.01.023zbMath1061.35103OpenAlexW1969709167MaRDI QIDQ1888004

Yanyan Li

Publication date: 22 November 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2004.01.023

zbMATH Keywords

attractorLyapunov exponentchaotic regimecascade of periodic solutionsdamped and forced Korteweg-de Vries equation

Mathematics Subject Classification ID

Attractors (35B41) KdV equations (Korteweg-de Vries equations) (35Q53) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (16)

The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus ⋮ Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform ⋮ A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS ⋮ A stability analysis of periodic solutions to the steady forced Korteweg-de Vries-Burgers equation ⋮ Long time behavior of solutions of gKdV equations ⋮ Global attractors for the Benjamin-Bona-Mahony equation with memory ⋮ Soliton interaction with external forcing within the Korteweg–de Vries equation ⋮ Chaotifing a linear hyperbolic system of partial differential equations by means of nonlinear boundary reflection ⋮ Damping to prevent the blow-up of the Korteweg-de Vries equation ⋮ Bifurcation and nonsmooth dynamics of solitary waves in the generalized long-short wave equations ⋮ Computation of time-periodic solutions of the Benjamin-Ono equation ⋮ A simple and robust boundary treatment for the forced Korteweg-de Vries equation ⋮ The global attractor and numerical simulation of a forced weakly damped MKdV equation ⋮ Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs ⋮ Generalized Korteweg-de Vries equation in \(H^1(\mathbb R)\) ⋮ Long-time behavior of solutions of a BBM equation with generalized damping

Uses Software

• PseudoPack

Cites Work

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• The evolution of resonant water-wave oscillations
• Periodic and chaotic behaviour in a reduction of the perturbed Korteweg-de Vries equation
• Evaluating the dimension of an inertial manifold for the Kuramoto-Sivashinsky equation.

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