TY - JOUR
T1 - Lump and Rogue Wave Solutions of a Reduced (3 + 1)-Dimensional Shallow Water Equation
AU - Jiayue Gu & Huanhe Dong
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 510
EP - 518
PY - 2018
DA - 2018/08
SN - 8
DO - http://doi.org/10.4208/eajam.271217.130318
UR - https://global-sci.org/intro/article_detail/eajam/12622.html
KW - Lump solution, rogue wave, (3+1)-dimensional shallow water equation, Hirota bilinear operator.
AB - <p style="text-align: justify;">Considering a reduced (3 + 1)-dimensional shallow water equation, we use
Hirota formulation and symbolic calculation to derive positive lump solitons rationally
localised in all directions of the $(x, y)$-plane. The interaction of the lump and one stripe
solitons is studied. Numerical experiments show that the collision of such solutions is
completely inelastic and the lump soliton is swallowed by the stripe one. Exploring the
interaction of the lump and a couple of resonance stripe solitons, we note that the lump
soliton transforms into a ghost soliton. Most of the time it remains hidden in stripe
solitons, but appears at a certain time and fades after that.</p>