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

Darryl D. Holm·Martin F. Staley
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Abstract

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 = νm_{xx} $ with $m = u - α^2 u_{xx}$ for fluid velocity $u(x,t)$ change their behavior at the special values $b=0,\pm1,\pm2,\pm3$.

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Darryl D. Holm, Martin F. Staley. 2003-01-29. Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary pde. https://doi.org/10.1016/s0375-9601(03)00114-2

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