Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary pde

By Darryl D. Holm, Martin F. Staley. 2002

164 citations recorded by the source corpus.

We study exchange of stability in the dynamics of solitary wave solutions under changes in the nonlinear balance in a 1+1 evolutionary partial differential equation related both to shallow water waves and to turbulence. We find that solutions of the equation mt + umx + buxm = � mxx with m = u � 2 uxx for fluid velocity u(x,t) change their behavior at the special values b = 0,±1,±2,±3.

Subfields: Mathematical Physics, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fdb5ec32829cbf9bc2e9538226bf1270fa6b25fb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

Stability of peakons for the Degasperis‐Procesi equation (2007, unknown): “A P] 1 2 D Keywords: Stabiltiy; Degasperis-Procesi equation; Peakons Mathematics Subject Classification (2000): 35G35, 35Q51, 35G25, 35L05”
On asymptotically equivalent shallow water wave equations (2003, background): “See [21] for discussions of equation (42) in which b is treated as a bifurcation parameter when c0 = 0 and Γ = 0.”
Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition (2007, background): “On the other hand, the DP equation has the well-known peakon solution [8] u(x, t) = U(ξ) = ce−|x−ct−ξ0| (ξ0 = x0 − ct0) with the following properties U(ξ0) = c, U(±∞) = 0, U ′(ξ0−) = c, U ′(ξ0+) = −c, (2.”
On the Blow-up Phenomena for the Degasperis–Procesi Equation (2010, unknown): “Mathematics Subject Classification (2000): 35G25, 35L05”