We consider nonlinear relativistic wave equations in one space dimension and prove the spreading rate estimates for a general class of potentials. Such estimates play an important role in studying the asymptotic stability of solitons.
References
V. S. Buslaev and G. S. Perelman, Scattering for the nonlinear Schrödinger equations: states close to a soliton. St. Petersburg Math. J. 4, no. 6 (1993) pp 1111-1142. MR1199635 V. S. Buslaev and G. S. Perelman, Scattering for the nonlinear Schrödinger equations: states close to a soliton. St. Petersburg Math. J. 4, no. 6 (1993) pp 1111-1142. MR1199635
V. S. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 20, no. 3 (2003), pp 419-475. MR1972870 10.1016/S0294-1449(02)00018-5 V. S. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 20, no. 3 (2003), pp 419-475. MR1972870 10.1016/S0294-1449(02)00018-5
M. Grillakis, J. Shatah, and W. A. Strauss, Stability theory of solitary waves in the presence of symmetry, I; II. J. Func. Anal. 74, no. 1 (1987), pp 160-197; 94 (1990), no. 2, pp 308-348. MR901236 0656.35122 10.1016/0022-1236(87)90044-9 M. Grillakis, J. Shatah, and W. A. Strauss, Stability theory of solitary waves in the presence of symmetry, I; II. J. Func. Anal. 74, no. 1 (1987), pp 160-197; 94 (1990), no. 2, pp 308-348. MR901236 0656.35122 10.1016/0022-1236(87)90044-9
A. Komech, N. J. Mauser, and A. Vinnichenko, On attraction to solitons in relativistic nonlinear wave equations. Russ. J. Math. Phys. 11, no. 3 (2004), pp 289-307. MR2133795 1186.35222 A. Komech, N. J. Mauser, and A. Vinnichenko, On attraction to solitons in relativistic nonlinear wave equations. Russ. J. Math. Phys. 11, no. 3 (2004), pp 289-307. MR2133795 1186.35222
A. Komech and E. Kopylova, On asymptotic stability of moving kink for relativistic Ginsburg-Landau equation. Comm. Math. Phys. 302, no. 1 (2011), pp 225-252. MR2770013 1209.35134 10.1007/s00220-010-1184-7 A. Komech and E. Kopylova, On asymptotic stability of moving kink for relativistic Ginsburg-Landau equation. Comm. Math. Phys. 302, no. 1 (2011), pp 225-252. MR2770013 1209.35134 10.1007/s00220-010-1184-7
A. Komech and E. Kopylova, On asymptotic stability of kink for relativistic Ginsburg-Landau equation. Arch. Rat. Mech. and Analysis 202, no. 2 (2011), pp 213-245. MR2835867 06101947 10.1007/s00205-011-0415-1 A. Komech and E. Kopylova, On asymptotic stability of kink for relativistic Ginsburg-Landau equation. Arch. Rat. Mech. and Analysis 202, no. 2 (2011), pp 213-245. MR2835867 06101947 10.1007/s00205-011-0415-1
M. Reed, Abstract Non-Linear Wave Equations. Lecture Notes in Mathematics 507, Springer, Berlin 1976. MR605679 0317.35002 M. Reed, Abstract Non-Linear Wave Equations. Lecture Notes in Mathematics 507, Springer, Berlin 1976. MR605679 0317.35002