TY - JOUR

T1 - Compact and noncompact dispersive patterns

AU - Rosenau, Philip

N1 - Funding Information:
I thank R. Camassa and P. Olver for a number of enjoyable and illuminative discussions. This work was supported in part by a grant from the Israel Science Foundation and carried out in part during a stay at The Center of Nonlinear Studies at the Los-Alamos National Laboratory and visit to The Courant Institute of Mathematical Sciences supported via Air-Force grant # F49620-98-1-0256.

PY - 2000/10/9

Y1 - 2000/10/9

N2 - 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. (C) 2000 Elsevier Science B.V.

AB - 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. (C) 2000 Elsevier Science B.V.

UR - http://www.scopus.com/inward/record.url?scp=0034626343&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(00)00577-6

DO - 10.1016/S0375-9601(00)00577-6

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AN - SCOPUS:0034626343

SN - 0375-9601

VL - 275

SP - 193

EP - 203

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3

ER -