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26 April 2024 |
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Wave Structures and Nonlinear Balances in a Family of 1+1 Evolutionary PDEs | | Darryl D. Holm
; Martin F. Staley
; | | Date: |
26 Feb 2002 | | Subject: | Chaotic Dynamics; Pattern Formation and Solitons | nlin.CD nlin.PS | | Abstract: | We study the following family of evolutionary 1+1 PDEs that describe the balance between convection and stretching for small viscosity in the dynamics of 1D nonlinear waves in fluids: m_t + underbrace{um_x _{(-2mm)hbox{convection}(-2mm)} + underbrace{b u_xm _{(-2mm)hbox{stretching}(-2mm)} = underbrace{
u m_{xx} }_{(-2mm)hbox{viscosity}}, quadhbox{with}quad u=g*m . Here $u=g*m$ denotes $ u(x)=int_{-infty}^infty g(x-y)m(y) dy . $ We study exchanges of stability in the dynamics of solitons, peakons, ramps/cliffs, leftons, stationary solutions and other solitary wave solutions associated with this equation under changes in the nonlinear balance parameter $b$. | | Source: | arXiv, nlin.CD/0202059 | | Services: | Forum | Review | PDF | Favorites | |
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