Nonlinear propagation of a partly coherent pulse in a fiber waveguide and the role of higher-order dispersion

1988 ◽  
Vol 18 (2) ◽  
pp. 207-211 ◽  
Author(s):  
Viktor A Aleshkevich ◽  
Victor A Vysloukh ◽  
G D Kozhoridze ◽  
A N Matveev ◽  
S I Terzieva
Keyword(s):  
Higher Order ◽  
Nonlinear Propagation ◽  
Fiber Waveguide ◽  
Coherent Pulse ◽  
Higher Order Dispersion ◽  
Order Dispersion

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

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