Wronskian solutions of the Boussinesq equation - Solitons, negatons, positons and complexitons

Inverse Problems

Volumn 23, Issue 1, 2007, Pages 279-296

  Li, Chun Xia ^a   Ma, Wen Xiu ^b   Liu, Xiao Jun ^a   Zeng, Yun Bo ^a  

^a TSINGHUA UNIVERSITY   (China)

^b UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; LINEAR EQUATIONS; PROBLEM SOLVING; SOLITONS;

BOUSSINESQ EQUATION; NEGATONS; WRONSKIAN FORMULATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33947640521     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/1/015     Document Type: Article

References (40)

1. Boussinesq J 1872 J. Math. Pures Appl. 17 55-108
2. Boussinesq J 1877 Mem. Pres. Acad. Sci. (Paris) 23 56-8
3. Whitham G B 1975 Linear and Nonlinear Waves (New York: Wiley-Interscience)
4. Xu L, Auston D H and Hasegawa A 1992 Phys. Rev. A 45 3184-93
5. Karpman V I 1975 Nonlinear Waves in Dispersive Media (New York: Pergamon)
6. Turitsyn S K and Fal'kovich G E 1985 Zh. Eksp. Teor. Fiz. 89 258-70
7. Turitsyn S K and Fal'kovich G E 1985 Sov. Phys.-JETP 62 146-52
8. Klein R, Mikusky E and Owinoh A 2005 Multiple scales asymptotics for atmospheric flows European Congress of Mathematics (Zürich: European Mathematical Society) pp 201-20
9. Constantin P 1999 Bounds for turbulent transport IUTAM Symposium on Geometry and Statistics of Turbulence (Hayama)
10. Constantin P 2001 Fluid Mechanics Applications vol 59 ed T Kambe, T Nakano and T Miyauchi (Dordrecht: Kluwer) pp 23-31
11. Zakharov V E 1973 Zh. Eksp. Teo. Fiz. 65 219-25
12. Zakharov V E 1974 Sov. Phys.-JETP 38 108-10
13. Kalantarov V K and Ladyzhenskaya O A 1978 J. Sov. Math. 10 53-70
14. Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
15. Hirota R 1973 J. Math. Phys. 14 810-4
16. Zhang J E and Li Y S 2003 Phys. Rev. E 67 016306
17. Ma W X 2002 Phys. Lett. A 301 35-44
18. Ma W X and You Y C 2005 Trans. Am. Math. Soc. 357 1753-78
19. Arkadiev V A, Pogrebkov A K and Polivanov M K 1984 Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 133 17-37 (in Russian)
20. Matveev V B 1992 Phys. Lett. A 166 205-8
21. Matveev V B 1992 Phys. Lett. A 166 209-12
22. Rasinariu C, Sukhatme U and Khare A 1996 J. Phys. A: Math. Gen. 29 1803-23
23. Kruskal M D 1974 Lectures on Applied Mathematics vol 15 (Providence, RI: American Mathematical Society) pp 61-83
24. Airault H, McKean H P and Moser J 1977 Commun. Pure Appl. Math. 30 95-148
25. Ablowitz M J and Cornille H 1979 Phys. Lett. A 72 277-80
26. Ma W X 2003 J. Phys. Soc. Japan 72 3017-9
27. Ma W X 2004 Chaos Solitons Fractals 19 163-70
28. Ma W X and Maruno K 2004 Phys. A 343 219-37
29. Maruno K, Ma W X and Oikawa M 2004 J. Phys. Soc. Japan 73 831-7
30. Xiao T and Zeng Y B 2004 J. Phys. A: Math. Gen. 37 7143-62
31. Shao Y J and Zeng Y B 2005 J. Phys. A: Math. Gen. 38 2441-67
32. Liu X J and Zeng Y B 2005 J. Phys. A: Math. Gen. 38 8951-65
33. Gegenhasi, Tam H W and Wang H Y 2006 Rep. Math. Phys. 58 195-205
34. Gegenhasi and Hu X B 2006 J. Nonlinear Math. Phys. 13 183-92
35. Wang H Y, Hu X B and Gegenhasi 2006 J. Comput. Appl. Math. at press
36. Ma W X Chaos Solitons Fractals 26 1453-8
37. Hirota R and Satsuma J 1976 Prog. Theor. Phys. Suppl. 59 64-100
38. Hirota R 1980 Direct Method in Soliton Theory ed R K Bullough and P J Caudrey (Berlin: Springer) pp 157-76
39. Freeman N C and Nimmo J J C 1983 Phys. Lett. A 95 1-3
40. Nimmo J J C and Freeman N C 1983 Phys. Lett. A 95 4-6