On a direct approach to quasideterminant solutions of a noncommutative KP equation

Gilson, Claire R.; Nimmo, J. J. C.; Sooman, C M

doi:10.1088/1751-8113/40/14/007

Cited by 86 publications

(101 citation statements)

References 32 publications

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“…for example [2,8,9,13,14]. Particularly close in spirit to the present paper are [5][6][7]10]). Our result on the general operator level is the following: THEOREM 1.…”

Section: Introduction and Main Resultssupporting

confidence: 72%

Explicit Solution Formulas for the Matrix-Kp

Schiebold¹

2009

Glasgow Math. J.

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Abstract. We study a non-commutative version of the Kadomtsev-Petviashvili equations and construct a family of solutions generalizing naturally the soliton to the non-commutative setting. From this we derive explicit solution formulas as well for the scalar as for the matrix-Kadomtsev-Petviashvili equation which still depend on operator parameters.2000 Mathematics Subject Classification. 39B42, 47J25, 37K10, 35C05.

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“…for example [2,8,9,13,14]. Particularly close in spirit to the present paper are [5][6][7]10]). Our result on the general operator level is the following: THEOREM 1.…”

Section: Introduction and Main Resultssupporting

confidence: 72%

Explicit Solution Formulas for the Matrix-Kp

Schiebold¹

2009

Glasgow Math. J.

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“…From Eq. (2.24), we have a more explicit form as [9,12]: Physical interpretation of the configurations is non-trivial because even when f (x) and…”

Section: Exact Soliton Solutionsmentioning

confidence: 99%

Noncommutative integrable systems and quasideterminants

Hamanaka

Xiu

Hu³

et al. 2010

AIP Conference Proceedings

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We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many noncommutative integrable equations, which are represented in terms of Strachan's products and quasi-determinants, respectively. We also present a relation to an noncommutative anti-self-dual Yang-Mills equation, and make comments on how "integrability" should be considered in noncommutative spaces.

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“…, n) is not a single entry but a 2 × 2 matrix (since the θ i are eigenfunctions of L, M ). The Wronskian-like quasideterminant in (4.7) is termed a quasiwronskian, see [11], and [7] for details of Wronskian determinants. For ease of notation, for integers i, j = 1, .…”

Section: Quasiwronskian Solution Of Ncds Using Darboux Transformationsmentioning

confidence: 99%