On the theory of internal waves of permanent form in fluids of great depth

Amick, C. J.

doi:10.1090/S0002-9947-1994-1145726-1

On the theory of internal waves of permanent form in fluids of great depth
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by C. J. Amick

Trans. Amer. Math. Soc. 346 (1994), 399-419

DOI: https://doi.org/10.1090/S0002-9947-1994-1145726-1

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References

Internal waves of permanent form in fluids of great depth

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Solitary internal waves in deep fluid

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Hiroaki Ono, Algebraic solitary waves in stratified fluids, J. Phys. Soc. Japan 39 (1975), no. 4, 1082–1091. MR 398275, DOI 10.1143/JPSJ.39.1082
C. J. Amick and J. F. Toland, On solitary water-waves of finite amplitude, Arch. Rational Mech. Anal. 76 (1981), no. 1, 9–95. MR 629699, DOI 10.1007/BF00250799
C. J. Amick and J. F. Toland, On periodic water-waves and their convergence to solitary waves in the long-wave limit, Philos. Trans. Roy. Soc. London Ser. A 303 (1981), no. 1481, 633–669. MR 647410, DOI 10.1098/rsta.1981.0231
C. J. Amick and J. F. Toland, Uniqueness and related analytic properties for the Benjamin-Ono equation—a nonlinear Neumann problem in the plane, Acta Math. 167 (1991), no. 1-2, 107–126. MR 1111746, DOI 10.1007/BF02392447
C. J. Amick and J. F. Toland, Uniqueness of Benjamin’s solitary-wave solution of the Benjamin-Ono equation, IMA J. Appl. Math. 46 (1991), no. 1-2, 21–28. The Brooke Benjamin special issue (University Park, PA, 1989). MR 1106251, DOI 10.1093/imamat/46.1-2.21
C. J. Amick and R. E. L. Turner, A global theory of internal solitary waves in two-fluid systems, Trans. Amer. Math. Soc. 298 (1986), no. 2, 431–484. MR 860375, DOI 10.1090/S0002-9947-1986-0860375-3
C. J. Amick and R. E. L. Turner, Small internal waves in two-fluid systems, Arch. Rational Mech. Anal. 108 (1989), no. 2, 111–139. MR 1011554, DOI 10.1007/BF01053459
David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443
D. P. Bennett, R. W. Brown, S. E. Stansfield, J. D. Stroughair, and J. L. Bona, The stability of internal solitary waves, Math. Proc. Cambridge Philos. Soc. 94 (1983), no. 2, 351–379. MR 715035, DOI 10.1017/S0305004100061193
N. K. Bary, A treatise on trigonometric series. Vols. I, II, A Pergamon Press Book, The Macmillan Company, New York, 1964. Authorized translation by Margaret F. Mullins. MR 0171116
S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II, Comm. Pure Appl. Math. 17 (1964), 35–92. MR 162050, DOI 10.1002/cpa.3160170104