On the initial value problem for the KPII equation with data that do not decay along a line

Nonlinearity

Volumn 17, Issue 5, 2004, Pages 1843-1866

  Villarroel, Javier ^a   Ablowitz, Mark J ^b  

^a UNIVERSITY OF SALAMANCA   (Spain)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4644231570     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/5/015     Document Type: Article

References (45)

1. Kadomtsev B B and Petviashvili V I 1970 Sov. Phys. Dokl. 15 539
2. Fokas A S and Ablowitz M J 1983 Stud. Appl. Math. 69 211
3. Segur H 1982 Mathematical Methods in Hydrodynamics and Integrability in Dynamical Systems ed M Tabor and Y M Treve AIP Conf. Proc. 88 211
4. Manakov S V 1981 Physica D 3 420
5. Ablowitz M J, Bar Yaacov D and Fokas A S 1983 Stud. Appl. Math. 69 135
6. Ablowitz M J and Fokas A S 1983 Lecture Notes in Physics vol 189 (Berlin: Springer) See also the contribution of Fokas A S and Ablowitz M J in the same lecture notes
7. Ablowitz M J and Fokas A S 1983 Lecture Notes in Physics vol 189 (Berlin: Springer) See also the contribution of Fokas A S and Ablowitz M J in the same lecture notes
8. Ablowitz M J and Segur H 1979 J. Fluid Mech. 92 691
9. Ablowitz M J and Villarroel J 1991 Stud. Appl. Math. 85 195
10. Boiti M, Pempinelli F and Pogrebkov S 1994 Inverse Problems 10 505
11. Fokas A S and Sung L-Y 1999 Math. Proc. Camb. Philos. Soc. 125 113
12. Ablowitz M J and Villarroel J 2004 Initial Value Problems and Solutions of the KP Equation, New Trends in Integrability (Dordrecht: Kluwer) pp 1-47
13. Manakov S V, Zakharov V E, Bordag L A, Its A R and Matveev V B 1977 Phys. Lett. A 63 205
14. Gorshov K A, Pelinovskii D E and Stepahyants Yu A 1993 JETP 77 237
15. Ablowitz M J and Villarroel J 1997 Phys. Rev. Lett. 78 570
16. Villarroel J and Ablowitz M J 2003 SIAM J. Math Anal. 34 1252-77
17. Villarroel J and Ablowitz M J 1999 Commun. Math. Phys. 207 1
18. Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia, PA: SIAM)
19. Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
20. Wickerhauser M 1987 Commun. Math. Phys. 108 67
21. Fokas A S and Sung L Y 1992 Inverse Problems 8 673
22. Satsuma J 1976 J. Phys. Soc. Japan 40 276
23. Boiti M, Pempinelli F, Pogrebkov A and Prinari B 1997 Inverse Problems 13 L7
24. Boiti M, Pempinelli F, Pogrebkov A and Prinari B 2001 Inverse Problems 17 937
25. Boiti M, Pempinelli F, Pogrebkov A and Prinari B 2001 Phys. Lett. A 285 307
26. Boiti M, Pempinelli F, Pogrebkov A and Prinari B 2002 J. Math. Phys. 43 1044
27. Prinari B 1999 Inverse scattering transform for the Kadomtse-PetviashvilKadomtse-Petviashvili equations PhD Thesis University of Lecce
28. Fokas A and Pogrebkov A 2003 Nonlinearity 18 771
29. Fokas A, Pelinovskii D E and Sulem C 2001 Physica D 152-153 189
30. Villarroel J and Ablowitz M J 2002 Stud. Appl Math. 109 151
31. Faddeev L 1963 J. Math. Phys. 4 72
32. Deift P and Trubowitz E 1979 Commun. Pure Appl. Math. 32 121
33. Marchenko V A 1986 Sturm Liouville Operators and Applications (Boston, MA: Birkhauser)
34. Petersen P and Van Groesen E 2000 Physica D 141 316
35. Miles J 1977 J. Fluid Mech. 79 157
36. Miles J 1977 J. Fluid Mech. 79 171
37. Medina E 2002 Lett. Math. Phys. 62 91
38. Mañas M, Alonso L and Medina E 2001 Theor. Math. Phys. 127 800
39. Mañas M, Alonso L and Medina E 2002 J. Phys. A: Math. Gen. Phys. 35 401
40. Isogima S, Willox R and Satsuma J 2002 J. Phys. A: Math. Gen. Phys. 35 6893
41. Hirota R, Ohta Y and Satsuma J 1988 Prog. Theor. Phys. 94 59
42. Biondini G and Kodama Y 2003 J. Phys. A: Math. Gen. Phys. 36 10519
43. Dryuma V 1974 Sov. Phys.-JETP 19 381
44. Ablowitz M J and Fokas A S 1997 Complex Variables, Introduction and applications (Cambridge: Cambridge University Press)
45. Villarroel J 2003 J. Theor. Math. Phys. 137 1753