Abstract
We study nonintegrable effects appearing in the higher order corrections of an asymptotic perturbation expansion for a given nonlinear wave equation, and show that the analysis of the higher order terms provides a sufficient condition for asymptotic integrability of the original equation. The nonintegrable effects, which we call “obstacles” to the integrability, are shown to result in an inelasticity in soliton interaction. The main technique used in this paper is an extension of the normal form theory developed by Kodama and the approximate symmetry approach proposed by Mikhailov. We also discuss the case of the KP equation with the higher order corrections, a quasi-two dimensional extension of weakly dispersive nonlinear waves.
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© 1997 Birkhäuser Boston
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Kodama, Y., Mikhailov, A.V. (1997). Obstacles to Asymptotic Integrability. In: Fokas, A.S., Gelfand, I.M. (eds) Algebraic Aspects of Integrable Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 26. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2434-1_9
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DOI: https://doi.org/10.1007/978-1-4612-2434-1_9
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