AKNS

AcronymDefinition
AKNSAl Khaleej National School (Dubai, United Arab Emirates)
AKNSAblowitz-Kaup-Newell-Segur system
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m], m [greater than or equal to] 0, in the AKNS setup or [[partial derivative].
We have now sufficient ingredients to discuss the AKNS hierarchy and its strict version.
Equations (20) are called the Lax equations of the AKNS hierarchy and the deformation Q satisfying these equations is called a solution of the hierarchy.
Since (22) correspond to the strict cutoff (10), they are called the Lax equations of the strict AKNS hierarchy and the deformation Z is called a solution of this hierarchy.
greater than or equal to]0] | m [greater than or equal to] 1} satisfy the zero curvature relations (24), then Z is a solution of the strict AKNS hierarchy.
m]}, we call this last set of equations also the zero curvature form of the AKNS hierarchy.
m]}, respectively, corresponding to, respectively, a solution Q of the AKNS hierarchy and a solution Z of the strict AKNS hierarchy, also other parts satisfy such relations.
m] | m [greater than or equal to] 0} of a solution Q of the AKNS hierarchy satisfy
m] | m [greater than or equal to] 0} of a solution Z of the strict AKNS hierarchy satisfy
To clarify the link with the AKNS equation, consider relation (23) for [m.
and the second equation becomes AKNS equations (4), if one has [[partial derivative].
For the AKNS hierarchy, this system, the linearization of the AKNS hierarchy, is as follows: take a potential solution Q of the form (17) and consider the system