Dissipative periodic and chaotic patterns to the KdV-Burgers and Gardner equations

DOI10.1016/j.chaos.2019.07.006zbMath1448.35449arXiv1905.12626OpenAlexW2963044061WikidataQ127447370 ScholiaQ127447370MaRDI QIDQ2213851

Stefan C. Mancas, Ronald L. Adams

Publication date: 3 December 2020

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.12626

zbMATH Keywords

chaosHopf bifurcationhomoclinic orbitKdV-Burgers equationGardner equationLyapunov coefficientShil'nikov's analysis

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)

Related Items (3)

Construction of invariant solutions and conservation laws to the \((2+1)\)-dimensional integrable coupling of the KdV equation ⋮ On the modified Gardner type equation and its time fractional form ⋮ Soliton transmutations in KdV-Burgers layered media

Cites Work

• Traveling-wave solutions for Korteweg-de Vries-Burgers equations through factorizations
• The complex cubic--quintic Ginzburg--Landau equation: Hopf bifurcations yielding traveling waves
• Determining Lyapunov exponents from a time series
• Elements of applied bifurcation theory.
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• CHEN'S ATTRACTOR EXISTS
• Shil'nikov's theorem-a tutorial

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