Spatial chaos in weakly dispersive and viscous media: A nonperturbative theory of the driven KdV-Burgers equation

DOI10.1016/0167-2789(96)00043-7zbMath0885.35111arXivchao-dyn/9603013OpenAlexW3105285021MaRDI QIDQ1919657

M. A. Malkov

Publication date: 23 July 1996

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

Full work available at URL: https://arxiv.org/abs/chao-dyn/9603013

zbMATH Keywords

chaotic attractorrepellerfractalweak chaoscapacity dimensionasymptotic travelling wave solution of the KdV-Burgers equationdeveloped chaos

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (6)

Dynamic behaviors and soliton solutions of the modified Zakharov-Kuznetsov equation in the electrical transmission line ⋮ A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS ⋮ Modulation theory for the steady forced KdV-Burgers equation and the construction of periodic solutions ⋮ Application of the homotopy analysis method for solving the variable coefficient KdV-Burgers equation ⋮ Multistable structure in a Korteweg-de Vries system driven by a solitary wave ⋮ On chaotic wave patterns in periodically forced steady-state KdVB and extended KdVB equations

Cites Work

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• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Repellers, semi-attractors, and long-lived chaotic transients
• Quantitative universality for a class of nonlinear transformations
• Formation and regular dynamics of shock-trains in the Burgers model
• Deterministic Nonperiodic Flow
• Non-linear dispersive waves

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