On a class of nonlinear dispersive-dissipative interactions
- Tel Aviv Univ. (Israel). School of Mathematical Sciences
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.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 555545
- Report Number(s):
- LA-UR-97-3281; CONF-9705192-; ON: DE98001328; TRN: AHC29802%%130
- Resource Relation:
- Conference: 17. CNLS annual conference on nonlinear waves and solitons in physical systems, Los Alamos, NM (United States), 12-16 May 1997; Other Information: PBD: 29 Jul 1997
- Country of Publication:
- United States
- Language:
- English
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