Periodic and chaotic behaviour in a reduction of the perturbed Korteweg-de Vries equation

DOI10.1098/rspa.1994.0045zbMath0810.65078OpenAlexW1991655132MaRDI QIDQ4307726

R. H. J. Grimshaw, Xin Tian

Publication date: 1 November 1994

Published in: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1994.0045

zbMATH Keywords

periodic solutionschaosKdV equationKorteweg-de Vries equationhomoclinic orbitssubharmonic instabilityMelnikov functionssubharmonic bifurcationshomoclinic crossingsperiodic-doubling bifurcationsMelnikov sequence

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) KdV equations (Korteweg-de Vries equations) (35Q53) Bifurcation theory for ordinary differential equations (34C23) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Dynamical systems and ergodic theory (37-XX)

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