Non-uniqueness for the Fokas–Olver–Rosenau–Qiao equation

Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation

“…According to (33), p 1 ðtÞ = −ðb + δÞ and p 2 ðtÞ = b are obtained. We introduce the symbol q to represent the difference between the positions of the two peakons, in 5 Advances in Mathematical Physics other words, q≐q 2 − q 1 .…”

“…Himonas and Mantzavinos [32] proved that the FORQ equation (also called mCH) is well posed in H s for s > 5/2. The nonuniqueness results of Himonas and Holliman [33] show that solutions to the Cauchy problem for the FORQ equation are not unique in H s when s < 3/2. At present, there is no theory to show the uniqueness for the FORQ equation in H s when 3/2 ≤ s ≤ 5/2.…”

Traveling Wave Solution of the Olver–Rosenau Equation Solved by Dynamics System

“…has been studied for a long time and achieved so many results, such as the solution of Cauchy initial value problem [1], Holder continuous [2], the algebro-geometric solutions [3], the Cauchy problem of the generalized equation [4], and the nonuniqueness for the equation [5]. A lot of solving methods for the nonlinear partial differential equation are discussed to be applied in engineering and practice areas, such as the sine-Gordon expansion method [6] and the travelling wave method and its conservation laws [7], and so many examples are in this regard.…”

Non-uniform continuity of the Fokas-Olver-Rosenau-Qiao equation in Besov spaces

“…The local well-posedness and ill-posedness for the Cauchy problem of the FORQ equation (1.1) in Sobolev spaces and Besov spaces were studied in the series of papers [11,12,13,4]. It was showed by Himonas-Mantzavinos [11] that the FORQ is well-posed in Sobolev space H s with s > 5 2 in the sense of Hadamard.…”