On the stability of solitary waves for classical scalar fields
Annales de l'I.H.P. Physique théorique, Tome 47 (1987) no. 3, pp. 309-336. 
@article{AIHPA_1987__47_3_309_0,
     author = {Blanchard, Ph. and Stubbe, J. and V\'azquez, L.},
     title = {On the stability of solitary waves for classical scalar fields},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {309--336},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {3},
     year = {1987},
     mrnumber = {921309},
     zbl = {0649.35076},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1987__47_3_309_0/}
}
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Blanchard, Ph.; Stubbe, J.; Vázquez, L. On the stability of solitary waves for classical scalar fields. Annales de l'I.H.P. Physique théorique, Tome 47 (1987) no. 3, pp. 309-336. http://archive.numdam.org/item/AIHPA_1987__47_3_309_0/

[1] J. Stubbe, Constrained minimization problems in Orlicz-spaces with application to minimum action solutions of non-linear scalar field equations in RN. Bielefeld University, BI-TP 86/10, 1986.

[2] J. Shatah, Stable Standing waves of Nonlinear Klein-Gordon equations. Comm. Math. Phys., t. 91, 1983, p. 313-327. | MR | Zbl

[3] J. Shatah and W. Strauss, Instability of nonlinear bound-States. Comm. Math. Phys., t. 100, 1985, p. 173-190. | MR | Zbl

[4] W. Strauss, Existence of solitary waves in higher dimensions. Comm. Math. Phys., t. 55, 1977, p. 149-162. | MR | Zbl

[5] H. Berestycki and P.L. Lions, Nonlinear Scalar Field Equations. I. Arch. Rat. Mech. Anal., t. 82, 1983, p. 313-345. | MR | Zbl

[6] H. Brezis and E.H. Lieb, Minimum Action Solution of some Vector field equation. Comm. Math. Phys., t. 96, 1984, p. 97-113. | MR | Zbl

[7] H. Pecher, Low energy scattering for nonlinear Klein-Gordon equations, preprint. | MR

[8] W. Strauss, On weak solutions of semilinear hyperbolic equations. An. Acad. brasil. Cienc., t. 42, 1970, p. 645-651. | MR | Zbl

[9] J. Ginibre and G. Velo, Non-linear evolution equations: Cauchy problem and scattering theory, BIBOS preprint 102/85, Bielefeld, 1985.

[10] J. Ginibre and G. Velo, On a class of Nonlinear Schrödinger equations. I. The Cauchy problem, General case. J. Funct. Anal., t. 32, 1979, p. 1-32. | MR | Zbl

[11] T. Cazenave and A. Haraux, Équations d'évolution avec non linéarité logarithmique. Aunals. Fac. Sci. Univ. Toulouse, t. 2, 1980, p. 21-55. | Numdam | MR | Zbl

[12] A. Haraux, Nonlinear Evolution Equations. Global Behaviour of Solutions. Lecture Notes in Mathematics, t. 841, Springer, Berlin, 1981. | MR | Zbl

[13] T.F. Morris, Classical confinement: field theories with spontaneously bounded domains. Had. J., t. 3, 1980, p. 1333-1359. | MR | Zbl

[14] G. Rosen, Dilation Covariance and Exact Solutions in Local Relativistic Field Theories. Phys. Rev., t. 183, 1969, p. 1186-1188.

[15] I. Bialynicki-Birula and J. Michielsky, Wave Equations with Logarithmic Non-linearities. Bull. Acad. Pol. Sci. Cl. II., t. 23, 1975, p. 461-466. | MR

[16] T.F. Morris, Classical Theory of Klein-Gordon equations with logarithmic non-linearities. Can. Journ. Phys., t. 56, 1978, p. 1405-1411. | MR | Zbl

[17] I. Bialynicki-Birula and J. Michielsky, Nonlinear Wave Mechanics, Ann. of Phys., t. 100, 1976, p. 62-93. | MR

[18] G. Marques and I. Ventura, Resonances within nonperturbative methods in field theories. Phys. Rev., t. D 14, 1975, p. 1056-1059.

[19] M. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates. Comm. Math. Phys., t. 87, 1983, p. 567-576. | MR | Zbl

[20] H. Berestycki and Th. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon nonlinéaires. C. R. Acad. Sc. Paris, t. 293, 1981, p. 489-492. | MR | Zbl

[21] T. Cazenave and P.L. Lions, Orbital Stability of Standing waves for some Nonlinear Schrödinger Equations. Comm. Math. Phys., t. 85, 1982, p. 549-561. | MR | Zbl

[22] M. Weinstein, Lyapunov Stability of Ground States of Nonlinear Dispersive Evolution equations. Comm. Pure Appl. Math., t. 39, 1986, p. 51-67. | MR | Zbl

[23] T. Cazenave, Stable solutions of the logarithmic Schrödinger equation. Nonlinear Analysis TMA, t. 7, 1983, p. 1127-1140. | MR | Zbl

[24] E.H. Lieb, Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation. Stud. Appl. Math., t. 57, 1977, p. 93-105. | MR | Zbl

[25] G. Ginibre and G. Velo, On a class of nonlinear Schrödinger equation with nonlocal interaction. Math. Zeitschrift, t. 170, 1980, p. 109-136. | MR | Zbl

[26] Ph Blanchard, J. Stubbe and L. Vázquez, On the stability of nonlinear spinor fields, Phys. Rev. D, to appear.

[27] G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles. J. Math. Phys., t. 5, 1964, p. 1252-1254. | MR

[28] M. Weinstein, Modulational stability of Ground states of nonlinear Schrödinger Equations. Siam J. Math. Anal., t. 16, 1985, p. 472-491. | MR | Zbl

[29] M. Grillakis, J. Shatah and W. Strauss, Stability Theory of Solitary Waves in the Presence of Symmetry, I. J. Funct. Anal., t. 74, 1987, p. 160-197. | MR | Zbl