Construction of dKP and BKP equations with self-consistent sources

Inverse Problems

Volumn 22, Issue 5, 2006, Pages 1903-1920

  Hu, Xing Biao ^a   Wang, Hong Yan ^a,b  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^b UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

[No Author keywords available]

Indexed keywords

PROBLEM SOLVING; SOLITONS; TWO DIMENSIONAL;

GRAM-TYPE PFAFFIAN SOLUTIONS; LATTICE EQUATIONS; SOLITON EQUATIONS WITH SELF-CONSISTENT SOURCES (SESCS);

NONLINEAR EQUATIONS;

EID: 33749019106     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/5/022     Document Type: Article

References (47)

1. Ablowitz M J and Clarkson M J 1991 Solitons, nonlinear evolution equations and inverse scattering London Mathematical Society Lecture Note Series vol 149 (Cambridge: Cambridge University Press)
2. Konopelchenko B G 1992 Introduction to Multidimensional Integrable Equations: The Inverse Spectral Transform in 2 + 1 Dimensions (New York: Plenum)
3. Konopelchenko B G 1993 Solitons in Multidimensions: Inverse Spectral Transform Method (River Edge, NJ: World Scientific)
4. Mel'nikov V K 1989 Interaction of solitary waves in the system described by the Kadomtsev-Petviashvili equation with a self-consistent source Commun. Math. Phys. 126 201-15
5. Hirota R and Ohta Y 1991 Hierarchies of coupled soliton equations. I J. Phys. Soc. Japan 60 798-809
6. Hirota R 2004 Direct Method in Soliton Theory (in English) edited and translated by A Nagai, J Nimmo and C Gilson (Cambridge: Cambridge University Press)
7. Mel'nikov V K 1983 On equations for wave interactions Lett. Math. Phys. 7 129-36
8. Mel'nikov V K 1988 Exact solutions of the Korteweg-de Vries equation with a self-consistent source Phys. Lett. A 128 488-92
9. Mel'nikov V K 1989 Capture and confinement of solitons in nonlinear integrable systems Commun. Math. Phys. 120 451-68
10. Mel'nikov V K 1990 Integration of the Korteweg-de Vries equation with a source Inverse Problems 6 233-46
11. Mel'nikov V K 1992 Integration of the nonlinear Schrödinger equation with a source Inverse Problems 8 133-47
12. Mel'nikov V K 1987 A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x,y plane Commun. Math. Phys. 112 639-52
13. Zeng Y B, Ma W X and Lin R L 2000 Integration of the soliton hierarchy with self-consistent sources J. Math. Phys. 41 5453-89
14. Zeng Y B, Ma W X and Shao Y J 2001 Two binary Darboux transformations for the KdV hierarchy with self-consistent sources J. Math. Phys. 42 2113-28
15. Antonowicz M and Rauch-Wojciechowski S 1993 Soliton hierarchies with sources and Lax representation for restricted flows Inverse Problems 9 201-15
16. Leon J and Latifi A 1990 Solution of an initial-boundary value problem for coupled nonlinear waves J. Phys. A: Math. Gen. 23 1385-403
17. Deng S F, Chen D Y and Zhang D J 2003 The multisoliton solutions of the KP equation with self-consistent sources J. Phys. Soc. Japan 72 2184-92
18. Ma W X and Strampp W 1994 An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems Phys. Lett. A 185 277-86
19. Ma W X and Zhou Z X 2001 Binary symmetry constraints of N-wave interaction equations in 1 + 1 and 2 + 1 dimensions J. Math. Phys. 42 4345-82
20. Zeng Y B, Ma W X and Lin R L 2000 Integration of the soliton hierarchy with self-consistent sources J. Math. Phys. 41 5453-89
21. Lin R L, Zeng Y B and Ma W X 2001 Solving the KdV hierarchy with self-consistent sources by inverse scattering method Physica A 291 287-98
22. Urasboev G U and Khasanov A B 2001 Integration of the Korteweg-de Vries equation with a self-consistent source in the presence of 'steplike' initial data Theor. Math. Phys. 129 1341-56
23. Ye S and Zeng Y B 2002 Integration of the modified Korteweg-de Vries hierarchy with an integral type of source J. Phys. A: Math. Gen. 35 L283-91
24. Zeng Y B 1994 New factorization of the Kaup-Newell hierarchy Physica D 73 171-88
25. Zeng Y B and Li Y S 1996 The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy Acta Math. Sin. 12 217-24
26. Zeng Y B, Shao Y J and Ma W X 2002 Integral-type Darboux transformation for the mKdV hierarchy with self-consistent sources Commun. Theor. Phys. 38 641-8
27. Ma W X 2003 Soliton, positon and negaton solutions to a Schrödinger self-consistent source equation J. Phys. Soc. Japan 72 3017-9
28. Xiao T and Zeng Y B 2004 Generalized Darboux transformations for the KP equation with self-consistent sources J. Phys. A: Math. Gen. 37 7143-62
29. Xiao T and Zeng Y B 2006 Bäcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources Inverse Problems 22 869-80
30. Xiao T and Zeng Y B 2005 A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources Physica A 353 38-60
31. Hase Y, Hirota R, Ohta Y and Satsuma J 1989 Soliton solutions of the Mel'nikov equations J. Phys. Soc. Japan 58 2713-20
32. Matsuno Y 1991 Bilinear Bäcklund transformation for the KdV equation with a source J. Phys. A: Math. Gen. 24 L273-7
33. Hu X B 1991 Nonlinear superposition formula of the KdV equation with a source J. Phys. A: Math. Gen. 24 5489-97
34. Hu X B 1996 The higher-order KdV equation with a source and nonlinear superposition formula Chaos Solitons Fractals 7 211-5
35. Matsuno Y 1990 KP equation with a source and its soliton solutions J. Phys. A: math. Gen. 23 L1235-9
36. Zhang D J 2002 The N-soliton solutions for the modified KdV equation with self-consistent sources J. Phys. Soc. Japan 71 2649-56
37. Zhang D J and Chen D Y 2003 The N-soliton solutions of the sine-Gordon equation with self-consistent sources Physica A 321 467-81
38. Zhang D J 2003 The N-soliton solutions of some soliton equations with self-consistent sources Chaos Solitons Fractals 18 31-43
39. Gegenhasi and Hu X B 2006 On a integrable differential-difference equation with a source J. Nonlinear Math. Phys. 13 183-92
40. Liu X J and Zeng Y B 2005 On the Toda lattice equation with self-consistent sources J. Phys. A: Math. Gen. 38 8951-65
41. Wang H Y, Hu X B and Gegenhasi 2007 2D Toda lattice equation with self-consistent sources: Casoratian type solution, bilinear Bäcklund transformation and Lax pair J. Comp. Appl. Math. at press
42. Ohta Y, Hirota R and Tsujimoto S 1993 Casorati and discrete Gram type determinant representation of solutions to the discrete KP hierarchy J. Phys. Soc. Japan 62 1872-86
43. Gilson C R, Nimmo J J C and Tsujimoto S 2001 Pfaffianization of the discrete KP equation J. Phys. A: Math. Gen. 34 10569-75
44. Date E, Jimbo M, Kashiwara M and Miwa T 1981 Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type Physica D 4 343-65
45. Date E, Jimbo M, Kashiwara M and Miwa T 1981 Transformation groups for soliton equations: VI. KP hierarchies of orthogonal and symplectic type J. Phys. Soc. Japan 50 3813
46. Hirota R 1989 Soliton solutions to the BKP equation: I. The pfaffian technique J. Phys. Soc. Japan 58 2285-96
47. Hirota R 1981 J. Phys. Soc. Japan 50 3785