%0 Journal Article 
%A Anco, Stephen C.
%A Nayeri, HamidReza
%A Recio Rodríguez, Elena
%T Travelling wave solutions on a non-zero background for the generalized Korteweg–de Vries equation
%D 2021
%@ 1751-8121
%U http://hdl.handle.net/10498/33278
%X 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.
%K solitary wave
%K non-zero background
%K heavy tail wave
%K exact solution
%K generalized KdV equation
%~ Universidad de Cádiz