Abstract
Chaos is frequently associated with orbits homoclinic to unstable modes of deterministic nonlinear PDEs. Bilinear Hirota method was successfully employed to obtain homoclinic solutions for NLS with periodic boundaries. We propose a new method to analytically generate homo-clinic solutions for integrable nonlinear PDEs. This approach resembles the dressing method known in the theory of solitons. The pole positions in the dressing factor are given by the complex double points of the Floquet spectrum associated with unstable modes of the nonlinear equation. As an example, we reproduce first the homoclinic orbit for NLS, and then obtain the homoclinic solution for the modified nonlinear Schrödinger equation solvable by the Wadati–Konno–Ichikawa spectral problem.
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Doktorov, E., Rothos, V. (2006). HOMOCLINIC ORBITS AND DRESSING METHOD. In: Faddeev, L., Van Moerbeke, P., Lambert, F. (eds) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. NATO Science Series, vol 201. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3503-6_6
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DOI: https://doi.org/10.1007/978-1-4020-3503-6_6
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