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Nonlinear dispersion and compact structures. (English) Zbl 0953.35501
Relaxing the distinguished ordering that underlies the derivation of soliton supporting equations leads to new equations endowed with nonlinear dispersion crucial for the formation and coexistence of compactons, solitons with a compact support, and conventional solitons. Vibrations of the anharmonic mass-spring chain lead to a new Boussinesq equation admitting compactons and compact breathers. The model equation \(u_t+[\delta u+3\gamma u^2/2+u^{1-\omega}(u^\omega u_x)_x]_x+\nu u_{txx}=0\) \((\omega,\nu,\delta,\gamma \text{const})\) admits compactons and for \(2\omega=\nu\gamma=1\) has a bi-Hamiltonian structure. The infinite sequence of commuting flows generates an integrable, compacton’s supporting variant of the Harry Dym equation.

35Q53 KdV equations (Korteweg-de Vries equations)
Full Text: DOI
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