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Zbl 1115.35365
Rosenau, Philip
Compact and noncompact dispersive patterns. (English)
[J] Phys. Lett., A 275, No. 3, 193-203 (2000). ISSN 0375-9601

Summary: We discuss the pivotal role played by the nonlinear dispersion in shaping novel, compact and noncompact patterns. It is shown that if the normal velocity of a planar curve is $U= - (k^{n})_{s}$, $n>1$, where $k$ is the curvature, then the solitary 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.

MSC 2000:: *35Q53 KdV-like equations
35Q51 Solitons

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Zentralblatt MATH Berlin [Germany]