2010
DOI: 10.1088/0266-5611/26/9/095007
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Solutions of matrix NLS systems and their discretizations: a unified treatment

Abstract: Using a bidifferential graded algebra approach to "integrable" partial differential or difference equations, a unified treatment of continuous, semi-discrete (Ablowitz-Ladik) and fully discrete matrix NLS systems is presented. These equations originate from a universal equation within this framework, by specifying a representation of the bidifferential graded algebra and imposing a reduction. By application of a general result, corresponding families of exact solutions are obtained that in particular comprise … Show more

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Cited by 49 publications
(75 citation statements)
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References 152 publications
(254 reference statements)
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“…We mention that matrix triplets to obtain NLS solutions also appear in a non-Marchenko context [41][42][43].…”
Section: Theorem 2 If P Is An Invertible Matrix Then ( a B C) Is mentioning
confidence: 99%
“…We mention that matrix triplets to obtain NLS solutions also appear in a non-Marchenko context [41][42][43].…”
Section: Theorem 2 If P Is An Invertible Matrix Then ( a B C) Is mentioning
confidence: 99%
“…As a close variant, the equation (2.1) with Q replaced by Q * , the adjoint of Q, is often considered in the literature (see [1], [5], [10] and references therein). For our needs the two approaches are essentially equivalent since we mainly use them to derive handy solution formulas.…”
Section: Construction Of Mps'smentioning
confidence: 99%
“…The solution formula used here was first obtained in [21], see also [25]. For related work we refer to [5], [10], [18]. Returning to a subtlety indicated above, we mention that formulas analogous to those used here give a natural access to the MPS's of the KdV.…”
mentioning
confidence: 98%
“…As in [1], the Fay identities, that we present next, are formulated in terms of the socalled 'almost-intertwining' matrices [16] that satisfy the 'rank one condition' [17,18], which is a particular case of the Sylvester equation (see [19,20,21,22,23]). …”
Section: Matrices and Shiftsmentioning
confidence: 99%
“…Comparing the last equation with (6.9), it is easy to conclude that the natural way to introduce the n-dependence is 21) which transforms the remaining equations, (6.16)-(6.19), into…”
Section: Soliton Solutions For the Alhmentioning
confidence: 99%