Classification of the line-soliton solutions of KPII

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 27, 2008, Pages

  Chakravarty, Sarbarish ^a   Kodama, Yuji ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48249154597     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/27/275209     Document Type: Article

References (28)

1. Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
2. Biondini G and Chakravarty S 2006 Soliton solutions of the Kadomtsev-Petviashvili II equation J. Math. Phys. 47 033514
3. Biondini G and Chakravarty S 2007 Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation Math. Comput. Simul. 74 237-50
4. Biondini G and Kodama Y 2003 On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy J. Phys. A: Math. Gen. 36 10519-36
5. Bóna M 2004 Combinatorics of Permutations (Boca Raton, FL: Chapman and Hall)
6. Chakravarty S and Kodama Y 2008 A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation Contemp. Math. (Preprint 0802.0524) at press
7. Chakravarty S and Kodama Y Combinatorics and geometry of the N-soliton solutions of the KP equation, in preparation
8. Corteel S 2007 Crossings and alignments of permutations Adv. Appl. Math. 38 149-63
9. Freeman N C 1980 Soliton interactions in two dimensions Adv. Appl. Mech. 20 1-37
10. Freeman N C and Nimmo J J C 1983 Soliton-solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: the Wronskian technique Phys. Lett. 95A 1-3
11. Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
12. Infeld E and Rowlands G 2000 Nonlinear Waves, Solitons and Chaos (Cambridge: Cambridge University Press)
13. Kadomtsev B B and Petviashvili V I 1970 On the stability of solitary waves in weakly dispersing media Sov. Phys.-Dokl. 15 539-41
14. Kasraoui A and Zeng J 2006 Distribution of crossings, nestings and alignments of two edges in matchings and partitions Elect. J. Comb. 13 R33, 1-12
15. Kodama Y 2004 Young diagrams and N-soliton solutions of the KP equation J. Phys. A: Math. Gen. 37 11169-90
16. Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
17. Medina E 2002 An N soliton resonance for the KP equation: interaction with change of form and velocity Lett. Math. Phys. 62 91-9
18. Miles J W 1977 Diffraction of solitary waves J. Fluid Mech. 79 171-9
19. Miwa T, Jimbo M and Date E 2000 Solitons: Differential Equations, Symmetries and Infinite-dimensional Algebras (Cambridge: Cambridge University Press)
20. Newell A C and Redekopp L 1977 Breakdown of Zakharov-Shabat theory and soliton creation Phys. Rev. Lett. 38 377-80
21. Novikov S P, Manakov S V, Pitaevskii L P and Zakharov V E 1984 Theory of Solitons. The Inverse Scattering Transform (New York: Plenum)
22. Ohkuma K and Wadati M 1983 The Kadomtsev-Petviashvili equation: the trace method and the soliton resonances J. Phys. Soc. Japan 52 749-60
23. Pashaev O and Francisco M 2005 Degenerate four virtual soliton resonance for the KP-II Theor. Math. Phys. 144 1022-9
24. Postnikov A 2006 Total positivity, Grassmannians, and networks Preprint math.CO/0609764
25. Roselle D P 1968 Permutations by number of rises and successions Proc. Am. Math. Soc. 19 8-16
26. Sato M 1981 Soliton equations as dynamical systems on an infinite dimensional Grassmannian manifold RIMS Kokyuroku 439 30-46
27. Stanley R P 1997 Enumerative Combinatorics (Cambridge Studies in Advanced Mathematics) vol 2 (Cambridge: Cambridge University Press)
28. Williams L K 2005 Enumeration of totally positive Grassmann cells Adv. Math. 190 319-42