Loading...

Analytical study of dissipative solitary waves

Dini, F ; Sharif University of Technology | 2008

929 Viewed
  1. Type of Document: Article
  2. DOI: 10.1088/0031-8949/77/02/025504
  3. Publisher: 2008
  4. Abstract:
  5. In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Green's function methods up to the third order. We present an example and discuss the asymptotic behavior of the Green's function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves. Applications of the model include weakly nonlinear solutions of terahertz Josephson plasma waves in layered superconductors and ablative Rayleigh-Taylor instability. © 2008 The Royal Swedish Academy of Sciences
  6. Keywords:
  7. Asymptotic stability ; Control nonlinearities ; Control theory ; Cubic boron nitride ; Differential equations ; Energy conversion ; Function evaluation ; Magnetic field effects ; Magnetohydrodynamics ; Mathematical models ; Nonlinear programming ; Numerical methods ; Phase space methods ; Plasma diagnostics ; Plasma stability ; Plasma waves ; Sedimentation ; Solutions ; Waves ; Analytical solutions ; Analytical study ; Asymptotic behaviors ; Bounded and unbounded solutions ; Cubic non linearities ; Dissipative waves ; Exact solutions ; First order derivatives ; Function methods ; Josephson plasmas ; Layered superconductors ; New class ; Non-linear regimes ; Nonlinear solutions ; phase spaces ; Rayleigh Taylor (RT) instabilities ; Solitary waves ; Terahertz (THz) ; Third-order ; Green's function
  8. Source: Physica Scripta ; Volume 77, Issue 2 , 2008 ; 00318949 (ISSN)
  9. URL: https://iopscience.iop.org/article/10.1088/0031-8949/77/02/025504/pdf