Explicit solutions to the Korteweg-de Vries equation on the half line

Inverse Problems

Volumn 22, Issue 6, 2006, Pages 2165-2174

  Aktosun, Tuncay ^a   Van Der Mee, Cornelis ^b  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; FUNCTION EVALUATION; INVERSE PROBLEMS; LINEAR ALGEBRA; SOLITONS;

ELEMENTARY FUNCTIONS; EXPLICIT SOLUTIONS; KORTEWEG-DE VRIES EQUATION;

INTEGRAL EQUATIONS;

EID: 33846076641     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/6/015     Document Type: Article

References (37)

1. Bona J L, Sun S M and Zhang B Y 2002 A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane Trans. Am. Math. Soc. 354 427-90
2. Fokas A S 2002 Integrable nonlinear evolution equations on the half-line Commun. Math. Phys. 230 1-39
3. Zabusky N J and Kruskal M D 1965 Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states Phys. Rev. Lett. 15 240-3
4. Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia, PA: SIAM)
5. Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (London: Cambridge University Press)
6. Gardner C S, Greene J M, Kruskal M D and Miura R M 1967 Method for solving the Korteweg-de Vries equation Phys. Rev. Lett. 19 1095-7
7. Marchenko V A 1988 Nonlinear Equations and Operator Algebras (Dordrecht: Reidel)
8. Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
9. Aktosun T 2005 Solitons and inverse scattering transform Mathematical Studies in Nonlinear Wave Propagation (Contemp. Math. vol 379) ed D P Clemence and G Tang (Providence, RI: American Mathematical Society) pp 47-62
10. Colliander J E and Kenig C E 2002 The generalized Korteweg-de Vries equation on the half line Commun. Partial Diff. Eqns 27 2187-266
11. Aktosun T, Klaus M and van der Mee C 1992 Explicit Wiener-Hopf factorization for certain nonrational matrix functions Integral Eqns Operator Theory 15 879-900
12. Wahlquist H D and Estabrook F B 1975 Prolongation structures and nonlinear evolution equations J. Math. Phys. 16 1-7
13. Konopel'chenko B G 1990 On exact solutions of nonlinear integrable equations via integral linearising transforms and generalised Bäcklund-Darboux transformations J. Phys. A: Math. Gen. 23 3761-8
14. Huang N N 1992 Darboux transformations for the Korteweg-de Vries equation J. Phys. A: Math. Gen. 25 469-83
15. 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. A 95 1-3
16. Matveev V B 1992 Generalized Wronskian formula for solutions of the KdV equations: first applications Phys. Lett. A 166 205-8
17. Carl B and Schiebold C 2000 Ein direkter Ansatz zur Untersuchung von Solitonengleichungen Jahresber. Deutsch. Math.-Verein. 102 102-48
18. Ma W-X and You Y 2005 Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions Trans. Am. Math. Soc. 357 1753-78
19. Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
20. Treibich A and Verdier J L 1990 Solitons elliptiques The Grothendieck Festschrift vol III (Progr. Math. vol 88) (Boston, MA: Birkhäuser Boston) pp 437-80
21. Gesztesy F and Weikard R 1998 Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies-an analytic approach Bull. Am. Math. Soc. (N.S.) 35 271-317
22. Gesztesy F, Unterkofler K and Weikard R 2006 An explicit characterization of Calogero-Moser systems Trans. Am. Math. Soc. 358 603-56
23. Ablowitz M J and Satsuma J 1978 Solitons and rational solutions of nonlinear evolution equations J. Math. Phys. 19 2180-6
24. Arkad'ev V A, Pogrebkov A K and Polivanov M K 1985 Singular solutions of the KdV equation and the inverse scattering method J. Math. Sci. 31 3264-79
25. Matveev V B 1992 Positon-positon and soliton-positon collisions: KdV case Phys. Lett. A 166 209-12
26. Kovalyov M 1998 Basic motions of the Korteweg-de Vries equation Nonlinear Anal. 31 599-619
27. Gohberg I, Kaashoek M A and Sakhnovich A L 1998 Sturm-Liouville systems with rational Weyl functions: explicit formulas and applications Integral Eqns Operator Theory 30 338-77
28. Jaworski M 1984 Breather-like solutions to the Korteweg-de Vries equation Phys. Lett. A 104 245-7
29. Mei J-q and Zhang H-q 2005 New soliton-like and periodic-like solutions for the KdV equation Appl. Math. Comput. 169 589-99
30. Aktosun T and Klaus M 2001 Inverse theory: problem on the line Scattering ed E R Pike and P C Sabatier (London: Academic) chapter 2.2.4 pp 770-85
31. Faddeev L D 1967 Properties of the S-matrix of the one-dimensional Schrödinger equation Am. Math. Soc. Transl. (Ser. 2) 65 139-66
32. Deift P and Trubowitz E 1979 Inverse scattering on the line Commun. Pure Appl. Math. 32 121-251
33. Marchenko V A 1986 Sturm-Liouville Operators and Applications (Basel: Birkhäuser)
34. Chadan K and Sabatier P C 1989 Inverse Problems in Quantum Scattering Theory 2nd edn (New York: Springer)
35. Bart H, Gohberg I and Kaashoek M A 1979 Minimal Factorization of Matrix and Operator Functions (Basel: Birkhäuser)
36. Coddington E A and Levinson N 1955 Theory of Ordinary Differential Equations (New York: McGraw-Hill)
37. http://omega.uta.edu/∼aktosun