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

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

2002-03-05

arxiv.org/abs/nlin/0203007v2

Nonlinear Sciences

Chaotic Dynamics

15 pages, 8 figures. For this replacement of the original submission, we: (1) Introduced key explanations that clarify the dif

Scientific paper

10.1016/S0375-9601(03)00114-2

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 $ m_t + um_x +b u_xm = \nu m_{xx} $ with $m = u - \alpha^2 u_{xx}$ for fluid velocity $u(x,t)$ change their behavior at the special values $b=0,\pm1,\pm2,\pm3$.

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