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• W1999784747 abstract "Traveling wave solutions to a class of dispersive models, u t − u t x x + u u x = θ u u x x x + ( 1 − θ ) u x u x x , are investigated in terms of the parameter θ , including two integrable equations, the Camassa–Holm equation, θ = 1 / 3 , and the Degasperis–Procesi equation, θ = 1 / 4 , as special models. It was proved in H. Liu and Z. Yin (2011) [39] that when 1 / 2 < θ ≤ 1 smooth solutions persist for all time, and when 0 ≤ θ ≤ 1 2 , strong solutions of the θ -equation may blow up in finite time, yielding rich traveling wave patterns. This work therefore restricts to only the range θ ∈ [ 0 , 1 / 2 ] . It is shown that when θ = 0 , only periodic travel wave is permissible, and when θ = 1 / 2 traveling waves may be solitary, periodic or kink-like waves. For 0 < θ < 1 / 2 , traveling waves such as periodic, solitary, peakon, peaked periodic, cusped periodic, or cusped soliton are all permissible." @default.
• W1999784747 created "2016-06-24" @default.
• W1999784747 creator A5055952405 @default.
• W1999784747 creator A5058850458 @default.
• W1999784747 date "2015-01-01" @default.
• W1999784747 modified "2023-10-08" @default.
• W1999784747 title "On traveling wave solutions of the θ-equation of dispersive type" @default.
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• W1999784747 doi "https://doi.org/10.1016/j.jmaa.2014.06.058" @default.
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