On quintic equations with a linear window

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Abstract

We study a quintic dispersive equation ut=[au2+b(uuxx+βux2)+c(uu4x+2q1uxu3x+q2uxx2)]x and show that if β=q1=-q2, it may be cast into vt=[vu]x, where v=, ω=2β+1 and is a fourth order linear operator. This enables to construct traveling patterns via superposition of solutions. A plethora of bell-shaped, multi-humped and asymmetric compacton, is found. Their interaction ranges from being almost elastic to a noisy one, including fusion of bell-shaped compactons and anti-compactons into robust asymmetric structures. A stationary, zero-mass, doublet-like compacton is found to be an attractor of topologically similar, zero-mass, excitations.

Original languageEnglish
Pages (from-to)135-141
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume380
Issue number1-2
DOIs
StatePublished - 8 Jan 2016

Keywords

  • Compactons
  • Exact linearization,
  • Interaction
  • Quintic dispersive waves
  • Solitons
  • Volterra-Lotke system

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