Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
Page(s) 131 - 145
DOI https://doi.org/10.1051/mmnp/20127211
Published online 29 February 2012
  1. J.L. Bona, A.S. Fokas. Initial-boundary-value problems for linear and integrable nonlinear dispersive equations. Nonlinearity, 21 (2008), T195-T203. [CrossRef]
  2. J.L. Bona, W.G. Pritchard, L.R. Scott. An evaluation of a model equation for water waves. Philos. Trans. R. Soc. Lond., A 302 (1981), 458–510.
  3. J. Bona, R. Winther. The Korteweg–de Vries equation, posed in a quarter–plane. SIAM J. Math. Anal., 14 (1983), 1056–1106. [CrossRef] [MathSciNet]
  4. R. Carroll, Q. Bu. Solution of the forced nonlinear Schrödinger (NLS) equation using PDE techniques. Appl. Anal., 41 (1991), 33–51. [CrossRef] [MathSciNet]
  5. C.K. Chu, L.W. Xiang, Y. Baransky. Solitary waves induced by boundary motion. Commun. Pure Appl. Math., 36 (1983), 495–504. [CrossRef]
  6. S. Clark, F. Gesztesy. Weyl-Titchmarsh M-function asymptotics for matrix-valued Schrödinger operators. Proc. Lond. Math. Soc., III. Ser., 82 (2001), 701–724. [CrossRef]
  7. S. Clark, F. Gesztesy, M. Zinchenko. Weyl-Titchmarsh theory and Borg-Marchenko-type uniqueness results for CMV operators with matrix-valued Verblunsky coefficients. Oper. Matrices, 1 (2007), 535–592. [CrossRef] [MathSciNet]
  8. A.S. Fokas. Integrable nonlinear evolution equations on the half-line. Comm. Math. Phys., 230 (2002), 1–39. [CrossRef] [MathSciNet]
  9. A.S. Fokas. A unified approach to boundary value problems. CBMS-NSF Regional Conference Ser. in Appl. Math. vol. 78. SIAM, Philadelphia, 2008.
  10. A.S. Fokas, J. Lenells. Explicit soliton asymptotics for the Korteweg–de Vries equation on the half-line. Nonlinearity, 23 (2010), 937–976. [CrossRef] [MathSciNet]
  11. G. Freiling, V. Yurko. Inverse Sturm–Liouville Problems and Their Applications. Nova Science Publishers, Huntington, N.Y., 2001.
  12. F. Gesztesy, B. Simon. On local Borg-Marchenko uniqueness results. Commun. Math. Phys., 211 (2000), 273–287. [CrossRef]
  13. F. Gesztesy, B. Simon. A new approach to inverse spectral theory. II. General real potentials and the connection to the spectral measure. Ann. of Math. (2), 152 (2000), 593–643. [CrossRef] [MathSciNet]
  14. I. Gohberg, M.A. Kaashoek, A.L. Sakhnovich. Sturm-Liouville systems with rational Weyl functions : explicit formulas and applications. Integr. Equ. Oper. Theory, 30 (1998), 338–377. [CrossRef]
  15. M. Kac, P. van Moerbeke. A complete solution of the periodic Toda problem. Proc. Natl. Acad. Sci. USA, 72 (1975), 2879–2880. [CrossRef]
  16. D.J. Kaup, H. Steudel. Recent results on second harmonic generation. Contemp. Math., 326 (2003), 33–48. [CrossRef]
  17. A. Kostenko, A. Sakhnovich, G. Teschl. Weyl-Titchmarsh theory for Schrödinger operators with strongly singular potentials. Int. Math. Res. Not. 2011, Art. ID rnr065, 49pp.
  18. P.C. Sabatier. Elbow scattering and inverse scattering applications to LKdV and KdV. J. Math. Phys., 41 (2000), 414–436. [CrossRef] [MathSciNet]
  19. P.C. Sabatier. Lax equations scattering and KdV. J. Math. Phys., 44 (2003), 3216–3225. [CrossRef] [MathSciNet]
  20. P.C. Sabatier. Generalized inverse scattering transform applied to linear partial differential equations. Inverse Probl., 22 (2006), 209–228. [CrossRef]
  21. A.L. Sakhnovich. Dirac type and canonical systems : spectral and Weyl-Titchmarsh fuctions, direct and inverse problems. Inverse Probl., 18 (2002), 331–348. [CrossRef] [MathSciNet]
  22. A.L. Sakhnovich. Second harmonic generation : Goursat problem on the semi-strip, Weyl functions and explicit solutions. Inverse Probl., 21 (2005), 703–716. [CrossRef] [MathSciNet]
  23. A.L. Sakhnovich. On the compatibility condition for linear systems and a factorization formula for wave functions. J. Differ. Equations, 252 (2012), 3658–3667. [CrossRef] [MathSciNet]
  24. A.L. Sakhnovich. Sine-Gordon theory in a semi-strip. Nonlinear Analysis, 75 (2012), 964–974. [CrossRef] [MathSciNet]
  25. L.A. Sakhnovich. Nonlinear equations and inverse problems on the semi-axis (Russian). Preprint 87.30. Mathematical Institute, Kiev, 1987.
  26. L.A. Sakhnovich. Evolution of spectral data, and nonlinear equations. Ukrain. Math. J., 40 (1988), 459–461. [CrossRef]
  27. L.A. Sakhnovich. Spectral Theory of Canonical Differential Systems. Method of Operator Identities. Operator Theory Adv. Appl. Ser. vol. 107. Birkhäuser, Basel, 1999.
  28. B.A. Ton. Initial boundary value problems for the Korteweg-de Vries equation. J. Differ. Equations 25 (1977), 288–309. [CrossRef]
  29. P.A. Treharne, A.S. Fokas. The generalized Dirichlet to Neumann map for the KdV equation on the half-line. J. Nonlinear Sci., 18 (2008), 191–217. [CrossRef] [MathSciNet]

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