Quasi-stationary perturbations of the KdV soliton

Journal of Physics A: Mathematical and General

Volumn 37, Issue 17, 2004, Pages 4753-4767

  Herman, Russell L ^a  

^a UNIVERSITY OF NORTH CAROLINA WILMINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442631249     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/17/007     Document Type: Article

References (30)

1. Ablowitz M J and Fokas A S 2003 Complex Variables: Introduction and Applications (Cambridge: Cambridge University Press)
2. Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia: SIAM)
3. Hassani S 1991 Foundations of Mathematical Physics (Boston: Allyn and Bacon)
4. Herman R L 1990 Resolution of the motion of a perturbed KdV soliton Inverse Problems 6 43-54
5. Herman R L 1990 The stochastic damped KdV equation J. Phys. A: Math. Gen. 23 1063-84
6. Herman R L 1990 A direct approach to studying soliton perturbations J. Phys. A: Math. Gen. 23 2327-62
7. Herman R L 1990 Conservation laws and the perturbed KdV equation J. Phys. A: Math. Gen. 23 4719-24
8. Johnson R S 1972 Some numerical solutions of a variable coefficient Korteweg-deVries equation (with applications to solitary wave development on a shelf) J. Fluid Mech. 54 81-91
9. Kakutani T 1971 Effect of an uneven bottom on gravity waves J. Phys. Soc. Japan. 30 272-6
10. Karpman V I 1979 Soliton evolution in the presence of perturbation Phys. Scr. 20 462-78
11. Karpman V I and Maslov E M 1977 A perturbation theory for the Korteweg-deVries equation Phys. Lett. A 60 307-8
12. Karpman V I and Maslov E M 1978 Structure of tails produced under the action of perturbations of solitons Sov. Phys.-JETP 48 252-8
13. Kaup D J 1976 A perturbation expansion for the Zakharov-Shabat inverse scattering transform SIAM J. Appl. Math. 31 121-33
14. Kaup D J 1976 Closure of the squared Zakharov-Shabat eigenstates J. Math. Anal. Appl. 54 849-64
15. Kaup D J and Newell A C 1978 Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory Proc. Roy. Soc. London A 361 413-46
16. Keener J P and McLaughlin D W 1977 Solitons under perturbations Phys. Rev. A 16 777-90
17. Kivshar Y S and Malomed B A 1989 Dynamics of solitons in nearly integrable systems Rev. Mod. Phys. 61 763-915
18. Knickerbocker C J and Newell A C 1980 Shelves and the Korteweg-deVries equation J. Fluid Mech. 98 803-18
19. Kodama Y and Ablowitz M J 1981 Perturbations of solitons and solitary waves Stud. Appl. Math. 64 225-45
20. Korteweg D J and DeVries G 1895 On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves Phil. Mag. 39 55-108
21. Lamb G L Jr 1980 Elements of Soliton Theory (New York: Wiley)
22. Leibovich S and Randall J D 1973 Amplification and decay of long nonlinear waves J. Fluid Mech. 53 481-93
23. Mann E 1997 The perturbed Korteweg-deVries equation considered anew J. Math. Phys. 38 3772-85
24. Menyuk C R 1986 Origin of solitons in the 'real' world Phys. Rev. A 33 4367-74
25. Newell A C 1980 The inverse scattering transform Solitons ed R K Bullough and P J Caudrey (New York: Springer) pp 177-242
26. Ott E and Sudan R N 1969 Damping of solitary waves Phys. Fluids 13 1432-4
27. Sachs R L 1984 Completeness of derivatives of squared Schrödinger eigenfunctions and explicit solutions of the linearized KdV equation SIAM J. Math. Anal. 14 674-83
28. Wheelon A D 1968 Tables of Summable Series and Integrals Involving Bessel Functions (San Francisco: Holden-Day)
29. Yan J and Tang Y 1996 Direct approach to the study of soliton perturbations Phys. Rev. E 54 6816-24
30. Yang J 2000 Complete eigenfunctions of linearized integrable equations expanded around a soliton solution J. Math. Phys. 41 6614-38