Termination points and homoclinic glueing for a class of inhomogeneous nonlinear ordinary differential equations

@article{Keeler2021TerminationPA,
  title={Termination points and homoclinic glueing for a class of inhomogeneous nonlinear ordinary differential equations},
  author={John T. S. Keeler and Mark G. Blyth and John R. King},
  journal={Nonlinearity},
  year={2021},
  volume={34},
  pages={532 - 561}
}
Solutions u(x) to the class of inhomogeneous nonlinear ordinary differential equations taking the form u″+u2=αf(x) for parameter α are studied. The problem is defined on the x line with decay of both the solution u(x) and the imposed forcing f(x) as |x| → ∞. The rate of decay of f(x) is important and has a strong influence on the structure of the solution space. Three particular forcings are examined primarily: a rectilinear top-hat, a Gaussian, and a Lorentzian, the latter two exhibiting… 

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