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All issues Volume 7 / No 2 (2012) Math. Model. Nat. Phenom., 7 2 (2012) 131-145 References
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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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  4. R. Carroll, Q. Bu. Solution of the forced nonlinear Schrödinger (NLS) equation using PDE techniques. Appl. Anal., 41 (1991), 33–51. [CrossRef] [MathSciNet] [Google Scholar]
  5. C.K. Chu, L.W. Xiang, Y. Baransky. Solitary waves induced by boundary motion. Commun. Pure Appl. Math., 36 (1983), 495–504. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  8. A.S. Fokas. Integrable nonlinear evolution equations on the half-line. Comm. Math. Phys., 230 (2002), 1–39. [CrossRef] [MathSciNet] [Google Scholar]
  9. A.S. Fokas. A unified approach to boundary value problems. CBMS-NSF Regional Conference Ser. in Appl. Math. vol. 78. SIAM, Philadelphia, 2008. [Google Scholar]
  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] [Google Scholar]
  11. G. Freiling, V. Yurko. Inverse Sturm–Liouville Problems and Their Applications. Nova Science Publishers, Huntington, N.Y., 2001. [Google Scholar]
  12. F. Gesztesy, B. Simon. On local Borg-Marchenko uniqueness results. Commun. Math. Phys., 211 (2000), 273–287. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  15. M. Kac, P. van Moerbeke. A complete solution of the periodic Toda problem. Proc. Natl. Acad. Sci. USA, 72 (1975), 2879–2880. [CrossRef] [Google Scholar]
  16. D.J. Kaup, H. Steudel. Recent results on second harmonic generation. Contemp. Math., 326 (2003), 33–48. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  18. P.C. Sabatier. Elbow scattering and inverse scattering applications to LKdV and KdV. J. Math. Phys., 41 (2000), 414–436. [CrossRef] [MathSciNet] [Google Scholar]
  19. P.C. Sabatier. Lax equations scattering and KdV. J. Math. Phys., 44 (2003), 3216–3225. [CrossRef] [MathSciNet] [Google Scholar]
  20. P.C. Sabatier. Generalized inverse scattering transform applied to linear partial differential equations. Inverse Probl., 22 (2006), 209–228. [CrossRef] [Google Scholar]
  21. A.L. Sakhnovich. Dirac type and canonical systems : spectral and Weyl-Titchmarsh fuctions, direct and inverse problems. Inverse Probl., 18 (2002), 331–348. [Google Scholar]
  22. A.L. Sakhnovich. Second harmonic generation : Goursat problem on the semi-strip, Weyl functions and explicit solutions. Inverse Probl., 21 (2005), 703–716. [Google Scholar]
  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. [Google Scholar]
  24. A.L. Sakhnovich. Sine-Gordon theory in a semi-strip. Nonlinear Analysis, 75 (2012), 964–974. [CrossRef] [MathSciNet] [Google Scholar]
  25. L.A. Sakhnovich. Nonlinear equations and inverse problems on the semi-axis (Russian). Preprint 87.30. Mathematical Institute, Kiev, 1987. [Google Scholar]
  26. L.A. Sakhnovich. Evolution of spectral data, and nonlinear equations. Ukrain. Math. J., 40 (1988), 459–461. [CrossRef] [Google Scholar]
  27. L.A. Sakhnovich. Spectral Theory of Canonical Differential Systems. Method of Operator Identities. Operator Theory Adv. Appl. Ser. vol. 107. Birkhäuser, Basel, 1999. [Google Scholar]
  28. B.A. Ton. Initial boundary value problems for the Korteweg-de Vries equation. J. Differ. Equations 25 (1977), 288–309. [CrossRef] [Google Scholar]
  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] [Google Scholar]

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