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in Taylor series the propagation constant b( x)( Eq.( 2)). The standard substitution reads as [ 54 ]:
X 1
k2 b k k! xk ¼ bðxÞ�b 1 x � b 0: ðA10Þ
With this procedure we can take into account leading order dispersive terms in equations( 3) and( 4). The full dispersion profile is thus embedded rewriting the linear operator ~ L as:
0 |
|
|
1 |
|
L~
B ðxÞ ¼
@
|
�a 0 1 � i þ i b0 FF ðxÞ�b0 1; FF x � b0 0; FF
|
|
C
A:
|
�a 0 2 � 2i þ i b 0 SH ðxÞþðb0 1; FF � 2b0 1; SH Þx � b0 0; SH |
ðA11Þ
A. 4 Codes implementation
The numerical implementation of the dynamical models presented in this work, has been fully developed by home-built codes using Julia language [ 72 ].