Stability theory of solitary waves in the presence of symmetry, I
Tóm tắt
Từ khóa
Tài liệu tham khảo
Akhmediev, 1982, Novel class of nonlinear surfaces waves: asymmetric modes in a symmetric layered structure, Soviet Phys. JETP, 56, 299
Berestycki, 1981, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non-linéaires, C. R. Acad. Sci., 293, 489
Bona, 1987, Stability and instability of solitary waves of KdV type
Cazenave, 1982, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85, 549, 10.1007/BF01403504
A. Floer and A. Weinstein, Non-spreading wave packets for the cubic Schrödinger equation with a bounded potential, preprint.
C. K. R. T. Jones, Instability of standing waves for nonlinear Schrödinger type equations, preprint.
C. K. R. T. Jones and J. V. Moloney, Instability of standing waves in nonlinear optical waveguides, Phy. Lett. A, to appear.
Maddocks, 1985, Restricted quadratic forms and constrained variational principles, SIAM J. Math. Anal., 16, 47, 10.1137/0516004
J. H. Maddocks, Stability and folds, preprint.
Reed, 1978, Vol. IV
Shatah, 1983, Stable standing waves of nonlinear Klein-Gordon equations, Comm. Math. Phys., 91, 313, 10.1007/BF01208779
Shatah, 1985, Unstable ground state of nonlinear Klein-Gordon equations, Trans. Amer. Math. Soc., 290, 701, 10.1090/S0002-9947-1985-0792821-7
Shatah, 1985, Instability of nonlinear bound states, Comm. Math. Phys., 100, 173, 10.1007/BF01212446
Weinstein, 1986, Liapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math., 39, 10.1002/cpa.3160390103
M. Weinstein, Stability analysis of ground states of nonlinear Schrödinger equations, preprint.