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Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional 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
Earlier work this paper cites.
1974
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J. Satsuma, A Wronskian representation of N N -soliton solutions of nonlinear evolution equations, J. Phys. Soc. Japan
1979
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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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N. Freeman, J. Nimmo, Soliton-solutions of the Korteweg-deVries and Kadomtsev-Petviashvili equations: the Wronskian technique, Phys. Lett. A 95 (1983), 1–3
1983
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S. Novikov, S. V. Manakov, L. P. Pitaevskii and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method
1984
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M. J. Ablowitz and P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering
1991
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L. A. Dickey, Soliton equations and Hamiltonian systems
1991
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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, Representation Theory, 2 (1998) 70-78
1998
Cited alongside, same era.
T. Miwa and M. Jimbo and E. Date, Solitons: differential equations, symmetries and infinite-dimensional algebras
2000
Cited alongside, same era.
S. Fomin, A. Zelevinsky, Cluster Algebras I: Foundations, J. Amer. Math. Soc. 15
2002
Cited alongside, same era.
G. Biondini, Y. Kodama, On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy, J. Phys. A: Math. Gen. 36 (2003), 10519–10536
2003
Cited alongside, same era.
R Hirota, The Direct Method in Soliton Theory
2004
Cited alongside, same era.
Y. Kodama, Young diagrams and N N -soliton solutions of the KP equation, J. Phys. A: Math. Gen
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, A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation, Contemp. Math., 471 (2008), 47–67
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
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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 solitons in shallow water, J. Phys. A: Math. Theor
2010
Later among the works it cites.
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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.
E. Steingrimsson, L. Williams, Permutation tableaux and permutation patterns, J. Comb. Th. A, 114, 2007, 211–234
2007
Cited alongside, same era.
M. Gross, Tropical geometry and mirror symmetry, book available at http://www.math.ucsd.edu/
Cited in the paper.
A. Knutson, T. Lam, and D. Speyer, Positroid varieties: juggling and geometry, to appear in Compositio
Cited in the paper.
D. Maclagan, B. Sturmfels, Introduction to Tropical Geometry, in preparation
Cited in the paper.
A. Dimakis, F. Müller-Hoissen, KP line-solitons and Tamari lattices, J. Phys. A: Math. Theor. 44 (2011), 025203 (49pp)
2011
Closest in time.
Y. Kodama, L. Williams, KP solitons, total positivity, and cluster algebras, Proc. Natl. Acad. Sci., published online ahead of print May 11, 2011, doi:10.1073/pnas.1102627108
2011
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K. Talaska, Combinatorial formulas for Γ \Gamma
2011
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Y. Kodama, L. Williams, The Deodhar decomposition of the Grassmannian and the regularity of KP solitons, Advances in Mathematics 244 (2013), 979–1032
2013
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