RT journal article
T1 Travelling wave solutions on a non-zero background for the generalized Korteweg–de Vries equation
A1 Anco, Stephen C.
A1 Nayeri, HamidReza
A1 Recio Rodríguez, Elena
A2 Matemáticas
K1 solitary wave
K1 non-zero background
K1 heavy tail wave
K1 exact solution
K1 generalized KdV equation
AB For the generalized p-power Korteweg–deVries equation, all non-periodic travellingwave solutions with non-zero boundary conditions are explicitly classifiedfor all integer powers p >=1. These solutions are shown to consist of: brightsolitary waves and static humps on a non-zero background for odd p; dark solitarywaves on a non-zero background and kink (shock) waves for even p in thedefocusing 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-zerobackground, for even p in the focussing case.An explicit physical parameterizationis given for each type of solution in terms of the wave speed c, backgroundsize b, and wave height/depth h. The allowed kinematic region for existence ofthe solutions is derived, and other main kinematic features are discussed. Analyticalformulas are presented in the higher power cases p = 3, 4, which arecompared to the integrable cases p = 1, 2.
PB IOP Publishing
SN 1751-8121
YR 2021
FD 2021
LK http://hdl.handle.net/10498/33278
UL http://hdl.handle.net/10498/33278
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026