scholarly journals OPTICAL SOLITONS WITH HIGHER ORDER DISPERSION BY SEMI-INVERSE VARIATIONAL PRINCIPLE

2010 ◽  
Vol 102 ◽  
pp. 337-350 ◽  
Author(s):  
Patrice D. Green ◽  
Daniela Milovic ◽  
Dawn A. Lott ◽  
Anjan Biswas
Keyword(s):  
Variational Principle ◽  
Optical Solitons ◽  
Higher Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

Optical Solitons with Higher Order Dispersion in a Log Law Media

2010 ◽  
Vol 31 (9) ◽  
pp. 1057-1062 ◽  
Author(s):  
Anjan Biswas ◽  
James E. Watson ◽  
Carl Cleary ◽  
Daniela Milovic
Keyword(s):  
Optical Solitons ◽  
Higher Order ◽  
Log Law ◽  
Higher Order Dispersion ◽  
Order Dispersion

Optical Solitons with Higher Order Dispersion and Full Nonlinearity in Non-Kerr Law Media

2015 ◽  
Vol 12 (11) ◽  
pp. 4632-4645
Author(s):  
Jose Vega-Guzman ◽  
Mohammad F Mahmood ◽  
Qin Zhou ◽  
Essaid Zerrad ◽  
Anjan Biswas ◽  
...  
Keyword(s):  
Optical Solitons ◽  
Higher Order ◽  
Kerr Law ◽  
Higher Order Dispersion ◽  
Full Nonlinearity ◽  
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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