scholarly journals Bright soliton dynamics for seventh degree nonlinear systems with higher-order dispersion

AIP Advances ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 085102
Author(s):  
Yunsong Guo ◽  
Quan Cheng ◽  
Yahia Okacha ◽  
Karmand Abdulla Ahmed ◽  
Ying Wang ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Higher Order ◽  
Bright Soliton ◽  
Soliton Dynamics ◽  
Higher Order Dispersion ◽  
Order Dispersion

scholarly journals Soliton dynamics for quantum systems with higher-order dispersion and nonlinear interaction

AIP Advances ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 065313
Author(s):  
Chen Chen ◽  
Yuqi Pan ◽  
Jiyuan Guo ◽  
Ying Wang ◽  
Guojun Gao ◽  
...  
Keyword(s):  
Nonlinear Interaction ◽  
Quantum Systems ◽  
Higher Order ◽  
Soliton Dynamics ◽  
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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