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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.

35Q53KdV-like (Korteweg-de Vries) equations
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