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Nonlinear dispersion and compact structures. (English) Zbl 0953.35501
Summary:
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.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations)
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##### References:
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