Traveling wave solutions of the Degasperis-Procesi equation. (English) Zbl 1068.35163

Lenells, Jonatan

J. Math. Anal. Appl. 306, No. 1, 72-82 (2005).

Summary: We classify all weak traveling wave solutions of the Degasperis-Procesi equation \[ u_t= u_{txx}+ 4uu_x= 3u_xu_{xx}+ uu_{xxx}, \quad x\in \mathbb R,\;t> 0. \] In addition to smooth and peaked solutions, the equation is shown to admit more exotic traveling waves such as cuspons, stumpons, and composite waves.

MSC:

35Q58	Other completely integrable PDE (MSC2000)
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Keywords:

traveling wave solutions; peaked solutions; cuspons

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