For citation:
Eleonskij V. M., Korolev V. G., Kulagin N. E. On the dynamic system generated by Whitham's equation with oscillating kernel. Izvestiya VUZ. Applied Nonlinear Dynamics, 1993, vol. 1, iss. 3, pp. 72-86.
On the dynamic system generated by Whitham's equation with oscillating kernel
The Whitham's equation possessing the fast—vanishing oscillating kernel is investigated. A possibility of the reducing of this equation is shown either to the differential equation of the fourth rate or to the nonintegrable dynamic system with two degrees of freedom. which permits an existence of singular point of «saddle—focus» type. The series of homoclinic loops of that point are found numerically. These loops are images of self-localized oscillating solutions of the Whitham's equation. The curves of points on the parametre plane are found, where the system permits an existence of «sharpened» solutions. These solutions are investigated analytically.
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