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Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation.
B. B. Kadomtsev and V. I. Petviashvili, On the stability of solitary waves in weakly dispersive media, Sov. Phys. - Dokl
1970
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M. Sato, Soliton equations as dynamical systems on an infinite dimensional Grassmannian manifold, RIMS Kokyuroku (Kyoto University) 439 (1981), 30–46
1981
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G. Lusztig, Total positivity in reductive groups, in: Lie theory and geometry: in honor of Bertram Kostant, Progress in Mathematics 123, Birkhauser, 1994
1994
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G. Lusztig, Total positivity in partial flag manifolds, Represent. Theory 2 (1998), 70-78
1998
Earlier work this paper cites.
S. Fomin, A. Zelevinsky, Cluster Algebras I: Foundations, J. Amer. Math. Soc. , 15 (2002), 497–529
2002
Earlier work this paper cites.
Y. Kodama, Young diagrams and N N -soliton solutions of the KP equation, J. Phys. A: Math. Gen
2004
Cited alongside, same era.
R Hirota, The Direct Method in Soliton Theory
2004
Cited alongside, same era.
G. Biondini and S. Chakravarty, Soliton solutions of the Kadomtsev-Petviashvili II equation, J. Math. Phys
2006
Cited alongside, same era.
J. Scott, Grassmannians and cluster algebras, Proc. London Math. Soc. (3) 92 (2006) 345–380
2006
Cited alongside, same era.
A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math.CO/060976v1
Cited in the paper.
S. Chakravarty, Y. Kodama, Classification of the line-solitons of KPII, J. Phys. A: Math. Theor. 41 (2008) 275209 (33pp)
2008
Later among the works it cites.
S. Chakravarty, Y. Kodama, Soliton solutions of the KP equation and applications to shallow water waves, Stud. Appl. Math. 123 (2009) 83–151
2009
Later among the works it cites.
A. Postnikov, D. Speyer, L. Williams, Matching polytopes, toric geometry, and the non-negative part of the Grassmannian, J. Alg. Combin., 30 (2009), 173–191
2009
Later among the works it cites.
Y. Kodama, KP soliton in shallow water, J. Phys. A: Math. Theor
2010
Later among the works it cites.
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