On asymptotic stability of solitary waves

Ablowitz, 1981 Gardner, 1967, Phys. Rev. Lett., 19, 1095, 10.1103/PhysRevLett.19.1095 Benjamin, 1972, 328, 153 Korteweg, 1895, Philos. Mag., 39, 422, 10.1080/14786449508620739 Coddington, 1955 A. Soffer and M.I. Weinstein, Multichannel nonlinear scattering theory for nonintegrable equations, Integrable Systems and Applications, in: Springer lecture notes in physics, Vol. 342, eds. M. Balabane, P. Lochak and C. Sulem. Soffer, 1990, Commun. Math. Phys., 133, 119, 10.1007/BF02096557 A. Soffer and M.I. Weinstein, Multichannel nonlinear scattering theory for nonintegrable equations II: The case of anisotropic potentials and data, J. Diff. Eq., in press. Rego, 1991, A class of eigenvalue problems with applications to solitary wave instabilities, IMA-Minneapolis preprint no. 863 Bona, 1975, 344, 363 Bona, 1987, 411, 395 Laedke, 1984, J. Plasma Phys., 32, 263, 10.1017/S0022377800002026 Weinstein, 1986, On the solitary wave of the generalized Korteweg-de Vries equation, Vol. 23 Weinstein, 1986, Commun. Pure Appl. Math., 39, 51, 10.1002/cpa.3160390103 Weinstein, 1987, Commun. P.D.E., 12, 1133, 10.1080/03605308708820522 Kodama, 1981, Stud. Appl. Math., 64, 225, 10.1002/sapm1981643225 Keener, 1977, Phys. Rev. A, 16, 777, 10.1103/PhysRevA.16.777 Newell, 1978, 127 Weinstein, 1985, SIAM J. Math. Anal., 16, 472, 10.1137/0516034 R.L. Pego and M.I. Weinstein, Asymptotic stability of solitary waves, in preparation. Peletier, 1971, On the stability of waves of nonlinear parabolic systems Sattinger, 1976, Adv. Math., 22, 312, 10.1016/0001-8708(76)90098-0 Alexander, 1990, Z. Reine Angew. Math., 410, 167 Evans, 1972, Indiana Univ. Math. J., 21, 877, 10.1512/iumj.1972.21.21071 Evans, 1972, Indiana Univ. Math. J, 22, 75, 10.1512/iumj.1972.22.22009 Evans, 1972, Indiana Univ. Math. J, 22, 577, 10.1512/iumj.1972.22.22048 Evans, 1975, Indiana Univ. Math. J., 24, 1169, 10.1512/iumj.1975.24.24096 Jones, 1984, Trans. Am. Math. Soc., 286, 431, 10.1090/S0002-9947-1984-0760971-6 Jeffrey, 1971, Indiana Univ. Math. J., 20, 463, 10.1512/iumj.1970.20.20039 Kato, 1983, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Vol. 8 Henry, 1981