@article{AIHPC_2007__24_4_539_0, author = {Liu, Yue and Ohta, Masahito and Todorova, Grozdena}, title = {Strong instability of solitary waves for nonlinear {Klein-Gordon} equations and generalized {Boussinesq} equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {539--548}, publisher = {Elsevier}, volume = {24}, number = {4}, year = {2007}, doi = {10.1016/j.anihpc.2006.03.005}, zbl = {1120.35013}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.005/} }
TY - JOUR AU - Liu, Yue AU - Ohta, Masahito AU - Todorova, Grozdena TI - Strong instability of solitary waves for nonlinear Klein-Gordon equations and generalized Boussinesq equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2007 SP - 539 EP - 548 VL - 24 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.005/ DO - 10.1016/j.anihpc.2006.03.005 LA - en ID - AIHPC_2007__24_4_539_0 ER -
%0 Journal Article %A Liu, Yue %A Ohta, Masahito %A Todorova, Grozdena %T Strong instability of solitary waves for nonlinear Klein-Gordon equations and generalized Boussinesq equations %J Annales de l'I.H.P. Analyse non linéaire %D 2007 %P 539-548 %V 24 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.005/ %R 10.1016/j.anihpc.2006.03.005 %G en %F AIHPC_2007__24_4_539_0
Liu, Yue; Ohta, Masahito; Todorova, Grozdena. Strong instability of solitary waves for nonlinear Klein-Gordon equations and generalized Boussinesq equations. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 4, pp. 539-548. doi : 10.1016/j.anihpc.2006.03.005. http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.005/
[1] Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sci. Paris 293 (1981) 489-492. | Zbl
, ,[2] Équations de champs scalaires euclidiens non linéaires dans le plan, C. R. Acad. Sci. Paris 297 (1983) 307-310. | MR | Zbl
, , ,[3] Nonlinear scalar field equations, Arch. Rat. Mech. Anal. 82 (1983) 313-345. | MR | Zbl
, ,[4] Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation, Comm. Math. Phys. 118 (1988) 15-29. | MR | Zbl
, ,[5] Théorie des ondes et de remous qui se propagent…, J. Math. Pures Appl. 17 (1872) 55-108. | JFM | Numdam
,[6] A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR | Zbl
, ,[7] R.E. Caflisch, Shallow water waves, Lecture notes, New York University, New York.
[8] Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, New York University, Courant Institute of Mathematical Sciences, American Mathematical Society, Providence, RI, 2003. | MR | Zbl
,[9] Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982) 549-561. | MR | Zbl
, ,[10] Stability of Coulomb systems with magnetic fields I. The one-electron atom, Comm. Math. Phys. 104 (1986) 251-270. | MR | Zbl
, , ,[11] The global Cauchy problem for the non linear Klein-Gordon equation, Math. Z. 189 (1985) 487-505. | Zbl
, ,[12] Stability theory of solitary waves in the presence of symmetry, I, J. Funct. Anal. 74 (1987) 160-197. | MR | Zbl
, , ,[13] Stability theory of solitary waves in the presence of symmetry, II, J. Funct. Anal. 94 (1990) 308-348. | MR | Zbl
, , ,[14] Uniqueness of positive solutions of in , Arch. Rational Mech. Anal. 105 (1989) 234-266. | MR | Zbl
,[15] Instability and nonexistence of global solutions to nonlinear wave equations of the form , Trans. Amer. Math. Soc. 192 (1974) 1-21. | MR | Zbl
,[16] On the lowest eigenvalue of the Laplacian for the intersection of two domains, Invent. Math. 74 (1983) 441-448. | MR | Zbl
,[17] Instability of solitary waves for generalized Boussinesq equations, J. Dynam. Differential Equations 5 (1993) 537-558. | MR | Zbl
,[18] Instability and blow-up of solutions to a generalized Boussinesq equation, SIAM J. Math. Anal. 26 (1995) 1527-1546. | MR | Zbl
,[19] Strong instability of solitary-wave solutions of a generalized Boussinesq equation, J. Differential Equations 164 (2000) 223-239. | MR | Zbl
,[20] Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation, Trans. Amer. Math. Soc. 353 (2000) 191-208. | Zbl
,[21] Strong instability of solitary-wave solutions to a Kadomtsev-Petviashvili equation in three dimensions, J. Differential Equations 180 (2002) 153-170. | Zbl
,[22] Strong instability of standing waves for nonlinear Klein-Gordon equations, Discrete Contin. Dynam. Syst. 12 (2005) 315-322. | Zbl
, ,[23] M. Ohta, G. Todorova, Strong instability of standing waves for nonlinear Klein-Gordon equation and Klein-Gordon-Zakharov system, Preprint. | Zbl
[24] Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975) 273-303. | MR | Zbl
, ,[25] Stable standing waves of nonlinear Klein-Gordon equations, Comm. Math. Phys. 91 (1983) 313-327. | Zbl
,[26] Unstable ground state of nonlinear Klein-Gordon equations, Trans. Amer. Math. Soc. 290 (1985) 701-710. | Zbl
,[27] Instability of nonlinear bound states, Comm. Math. Phys. 100 (1985) 173-190. | MR | Zbl
, ,[28] Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977) 149-162. | MR | Zbl
,[29] Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983) 567-576. | MR | Zbl
,[30] Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39 (1986) 51-68. | MR | Zbl
,Cité par Sources :