# 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…

## References

SHOWING 1-10 OF 14 REFERENCES

On the critical free-surface flow over localised topography

- MathematicsJournal of Fluid Mechanics
- 2017

Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far field, and their stability. Using the forced…

Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

- EngineeringFluids
- 2019

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g.,…

Free surface flow over bottom topography

- Mathematics
- 2018

This thesis explores flow in a channel over a bottom topography. In particular, the problem of finding the shape of the unknown free-surface if the bottom topography is prescribed forms the main…

Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1998

A technique for calculating exponentially small terms beyond all orders in singularly perturbed ordinary differential equations is presented. The approach is based on the application of a WKBJ–type…

Green's Functions and Boundary Value Problems

- Mathematics
- 1979

Preface to Third Edition. Preface to Second Edition. Preface to First Edition. 0 Preliminaries. 0.1 Heat Conduction. 0.2 Diffusion. 0.3 Reaction-Diffusion Problems. 0.4 The Impulse-Momentum Law: The…

Free-surface flow over bottom topography PhD Thesis University of East Anglia/Univeristy of Adelaide

- 2018

Free-surface flow over bottom topography, University of East Anglia/Univeristy of Adelaide, PhD Thesis

- 2018

Wave Motion (Cambridge

- 2000