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Asymptotic estimates of solutions of the Sine-Gordon equation on right half lines almost linearly moving leftward

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1232)

Keywords

  • Inverse Scattering
  • Vries Equation
  • Half Line
  • Coordinate Region
  • Nonnegative Constant

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References

  1. M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, Method for solving the sine-Gordon equation, Phys. Rev. Lett. 30 (1973), 1262–1264.

    CrossRef  ADS  MathSciNet  Google Scholar 

  2. M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, The inverse scattering transform — Fourier analysis for nonlinear problems, Stud. Appl. Math. 53 (1974), 249–315.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, Philadelphia, SIAM, 1981.

    CrossRef  MATH  Google Scholar 

  4. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series, No. 55, U.S. Department of Commerce, 1964.

    Google Scholar 

  5. D.J. Kaup and A.C. Newell, The Goursat and Cauchy problems for the sine-Gordon equation, SIAM J. Appl. Math. 34 (1978), 37–54.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. G.L. Lamb, Jr., Elements of Soliton Theory, Wiley-Interscience, 1980.

    Google Scholar 

  7. G.L. Lamb, Jr. and D.W. McLaughlin, Aspects of soliton physics, in: Solitons (Ed. R.K. Bullough and P.J. Caudrey) Topics in Current Physics 17, Springer-Verlag, New York, 1980.

    CrossRef  Google Scholar 

  8. M. Ohmiya, On the generalized soliton solutions of the modified Korteweg-de Vries equation, Osaka J. Math. 11 (1974), 61–71.

    MathSciNet  MATH  Google Scholar 

  9. P. Schuur, On the approximation of a real potential in the Zakharov-Shabat system by its reflectionless part, preprint 341, Mathematical Institute Utrecht (1984).

    Google Scholar 

  10. P. Schuur, Decomposition and estimates of solutions of the modified Korteweg-de Vries equation on right half lines slowly moving leftward, preprint 342, Mathematical Institute Utrecht (1984).

    Google Scholar 

  11. S. Tanaka, Non-linear Schrödinger equation and modified Korteweg-de Vries equation; construction of solutions in terms of scattering data, Publ. R.I.M.S. Kyoto Univ. 10 (1975), 329–357.

    CrossRef  MATH  Google Scholar 

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© 1986 Springer-Verlag

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Schuur, P.C. (1986). Asymptotic estimates of solutions of the Sine-Gordon equation on right half lines almost linearly moving leftward. In: Asymptotic Analysis of Soliton Problems. Lecture Notes in Mathematics, vol 1232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073062

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  • DOI: https://doi.org/10.1007/BFb0073062

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17203-1

  • Online ISBN: 978-3-540-47387-9

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