Analytical novel solutions to the fractional optical dynamics in a medium with polynomial law nonlinearity and higher order dispersion with a new local fractional derivative

2021 ◽  
pp. 127744
Author(s):  
H. Yépez-Martínez ◽  
Mostafa M.A. Khater ◽  
Hadi Rezazadeh ◽  
Mustafa Inc
Keyword(s):  
Fractional Derivative ◽  
Higher Order ◽  
Local Fractional Derivative ◽  
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.

scholarly journals Stability in turbulence: The interplay between shocks and vorticity in a superfluid with higher-order dispersion

2020 ◽  
Vol 102 (5) ◽  
Author(s):  
M. E. Mossman ◽  
E. S. Delikatny ◽  
Michael McNeil Forbes ◽  
P. Engels
Keyword(s):  
Higher Order ◽  
Higher Order Dispersion ◽  
Order Dispersion
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