@misc{10498/33278,
year = {2021},
url = {http://hdl.handle.net/10498/33278},
abstract = {For the generalized p-power Korteweg–deVries equation, all non-periodic travelling
wave solutions with non-zero boundary conditions are explicitly classified
for all integer powers p >=1. These solutions are shown to consist of: bright
solitary waves and static humps on a non-zero background for odd p; dark solitary
waves on a non-zero background and kink (shock) waves for even p in the
defocusing case; pairs of bright/dark solitary waves on a non-zero background,
and also bright and dark heavy-tail waves (with power decay) on a non-zero
background, for even p in the focussing case.An explicit physical parameterization
is given for each type of solution in terms of the wave speed c, background
size b, and wave height/depth h. The allowed kinematic region for existence of
the solutions is derived, and other main kinematic features are discussed. Analytical
formulas are presented in the higher power cases p = 3, 4, which are
compared to the integrable cases p = 1, 2.},
publisher = {IOP Publishing},
keywords = {solitary wave},
keywords = {non-zero background},
keywords = {heavy tail wave},
keywords = {exact solution},
keywords = {generalized KdV equation},
title = {Travelling wave solutions on a non-zero background for the generalized Korteweg–de Vries equation},
doi = {10.1088/1751-8121/abda77},
author = {Anco, Stephen C. and Nayeri, HamidReza and Recio Rodríguez, Elena},
}