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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. (English) Zbl 1010.35066
Summary: 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 $m_t+um_x+bu_xm=\nu m_{xx}$ with $m=u-\alpha^2u_{xx}$ for fluid velocity $u(x,t)$ change their behavior at the special values $b=0,\pm 1,\pm 2,\pm 3$.

MSC:
35L05Wave equation (hyperbolic PDE)
74J35Solitary waves (solid mechanics)
35L70Nonlinear second-order hyperbolic equations
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References:
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