Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.J. Ablowitz and H. Segur, Asymptotic solutions of the Korteweg-de Vries equation, Stud. Appl. Math. 57 (1977), 13–44.
M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, Philadelphia, SIAM, 1981.
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.
A. Cohen, Existence and regularity for solutions of the Korteweg-de Vries equation, Arch. for Rat. Mech. and Anal. 71 (1979), 143–175.
P.J. Davis, Interpolation and Approximation, Dover, New York, 1963.
P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), 121–251.
W. Eckhaus and A. van Harten, The Inverse Scattering Transformation and the Theory of Solitons, North-Holland Mathematics Studies 50, 1981.
W. Eckhaus and P. Schuur, The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions, Math. Meth. in the Appl. Sci. 5 (1983), 97–116.
C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett. 19 (1967), 1095–1097.
C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura, Korteweg-de Vries equation and generalizations VI, Comm. Pure Appl. Math. 27 (1974), 97–133.
L. Landau and E. Lifschitz, Quantum Mechanics, Nonrelativistic Theory, Pergamon Press, New York, 1958.
P.D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968), 467–490.
J.W. Miles, The asymptotic solution of the Korteweg-de Vries equation in the absence of solitons, Stud. Appl. Math. 60 (1979), 59–72.
F.W. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974.
S. Tanaka, On the N-tuple wave solutions of the Korteweg-de Vries equation, Publ. R.I.M.S. Kyoto Univ. 8 (1972), 419–427.
S. Tanaka, Korteweg-de Vries equation; asymptotic behavior of solutions, Publ. R.I.M.S. Kyoto Univ. 10 (1975), 367–379.
N.J. Zabusky, Solitons and bound states of the time-independent Schrödinger equation, Phys. Rev. 168 (1968), 124–128.
V.E. Zakharov and L.D. Faddeev, Korteweg-de Vries equation, a completely integrable Hamiltonian system, Funct. Anal. Appl. 5 (1971), 280–287.
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this chapter
Cite this chapter
Schuur, P.C. (1986). Asymptotic estimates of solutions of the Korteweg-de Vries equation on right half lines slowly moving to the left. In: Asymptotic Analysis of Soliton Problems. Lecture Notes in Mathematics, vol 1232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073057
Download citation
DOI: https://doi.org/10.1007/BFb0073057
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17203-1
Online ISBN: 978-3-540-47387-9
eBook Packages: Springer Book Archive