On a Korteweg–de Vries-like equation with higher degree non-linearity

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

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On a Korteweg–de Vries-like equation with higher degree non-linearity

Cited by 4 publications

References 11 publications

The elliptic core of nonlinear oscillators

The elliptic core of nonlinear oscillators

Closed form integration of a hyperelliptic, odd powers, undamped oscillator

The 2-D Sextic Hamiltonian Oscillator

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