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
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AN - SCOPUS:0041439271
SN - 0375-9601
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
IS - 5-6
ER -