TY - JOUR

T1 - On nonanalytic solitary waves formed by a nonlinear dispersion

AU - Rosenau, Philip

N1 - Funding Information:
I am grateful to Slava Krylov and Iddo Carmen for their help with the graphical issues and to Peter Olver and Y.A. Li for a number of valuable observations regarding the peakons. This work was supported in part by the US-Israel BSF Grant #/94-00283.

PY - 1997/6/23

Y1 - 1997/6/23

N2 - We study the prototypical, genuinely nonlinear, K(m,n) equation, ut ± a(um)x + (un)xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m,n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.

AB - We study the prototypical, genuinely nonlinear, K(m,n) equation, ut ± a(um)x + (un)xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m,n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.

UR - http://www.scopus.com/inward/record.url?scp=0041439271&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(97)00241-7

DO - 10.1016/S0375-9601(97)00241-7

M3 - מאמר

AN - SCOPUS:0041439271

VL - 230

SP - 305

EP - 318

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

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

SN - 0375-9601

IS - 5-6

ER -