R L Herman 1990 J. Phys. A: Math. Gen. 23 2327 doi:10.1088/0305-4470/23/12/017
R L Herman
Show affiliationsStarting with an integrable nonlinear evolution equation, the author investigates perturbations about a one-soliton solution, through the inversion of a linear equation for the first-order correction to the soliton solution. This inversion differs from past methods, as the proposed method takes place in coordinate space, not spectral space, while it employs some of the tools of inverse scattering theory. The method is applied to the Korteweg-de Vries, nonlinear Schrodinger and sine-Gordon equations. The first-order corrections are then obtained.
35Q51 Solitons (See also 37K40)
35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
Issue 12 (21 June 1990)
R L Herman 1990 J. Phys. A: Math. Gen. 23 2327
Patricia Kenzelmann et al 2009 IOP Conf. Ser.: Earth Environ. Sci. 6 452017
R L Herman 1990 J. Phys. A: Math. Gen. 23 4719
R L Herman 1991 J. Phys. A: Math. Gen. 24 1161
R L Herman 1990 J. Phys. A: Math. Gen. 23 1063
R. Buta et al. 2003 The Astronomical Journal 126 1148
C Farrell and U Leonhardt 2005 J. Opt. B: Quantum Semiclass. Opt. 7 1
R L Herman 1990 Inverse Problems 6 43
Grégoire Misguich and Philippe Sindzingre 2007 J. Phys.: Condens. Matter 19 145202
F Radicchi et al 2008 J. Phys. A: Math. Theor. 41 224010