Compact and noncompact dispersive patterns
نویسنده
چکیده
We discuss the pivotal role played by the nonlinear dispersion in shaping novel, compact and noncompact patterns. It is Ž n. shown that if the normal velocity of a planar curve is Usy k , n)1, where k is the curvature, then the solitary s disturbances may propagate like compactons. We extend the KP and the Boussinesq equations to include nonlinear dispersion to the effect that the new equations support compact and semi-compact solitary structures in higher dimensions. We also discuss the relations between equations sharing the same scaling. We show how compacton supporting equations may be cast into a strong formulation wherein one avoids dealing with weak solutions. q 2000 Elsevier Science B.V. All rights reserved.
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