On a class of nonlinear dispersive-dissipative interactions

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The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found ... continued below

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45 p.

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Rosenau, P. July 29, 1997.

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  • Rosenau, P. Tel Aviv Univ. (Israel). School of Mathematical Sciences

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Description

The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.

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45 p.

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OSTI as DE98001328

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  • 17. CNLS annual conference on nonlinear waves and solitons in physical systems, Los Alamos, NM (United States), 12-16 May 1997

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  • Other: DE98001328
  • Report No.: LA-UR--97-3281
  • Report No.: CONF-9705192--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 555545
  • Archival Resource Key: ark:/67531/metadc690579

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  • July 29, 1997

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  • Aug. 14, 2015, 8:43 a.m.

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  • March 1, 2016, 6:10 p.m.

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Rosenau, P. On a class of nonlinear dispersive-dissipative interactions, article, July 29, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc690579/: accessed December 12, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.