Traveling wave solutions of the Degasperis-Procesi equation

By Jonatan Lenells. 2005

232 citations recorded by the source corpus.

We classify all weak traveling wave solutions of the Degasperis-Procesi equation. In addition to smooth and peaked solutions, the equation is shown to admit more exotic traveling waves such as cuspons, stumpons, and composite waves.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4b9ed9f2abb241bd23d9b50745a1966b20637de0

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “Recently, Lenells [32] classified all weak traveling wave solutions.”
Inverse scattering transform for the Degasperis–Procesi equation (2010, background): “Due to the presence of a peak at the wave crest, these waves have to be understood as weak solutions [42].”
Equations with Peakon Traveling Wave Solutions (2013, background): “For related results about them, we refer the reader to [2, 5–15, 17–19, 21] and the references therein.”
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, unknown): “properties for CH type and related nonlinear evolution equations, we refer the reader to [12], [13], [11], [15], [16], [6], [23], [49], [53], [50], [17], [45], [8], [42], [43], [44], [4], [3], [64], [18], [5], [47], [48], [10], [9], [70], and the references therein.”
On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, unknown): “Mathematics Subject Classification (2000): 35G25, 35L05”
Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition (2007, background): “Later in [10], Lenells also studied the traveling wave solitary solutions of the DP equation, which decay to zero at both infinities, but did not give explicit soliton solutions, either.”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “Recently, Lenells [31] classified all weak traveling wave solutions.”