TY - JOUR
T1 - Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena
AU - Ali , Mohamed R.
AU - Ma , Wen-Xiu
AU - Sadat , R.
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 201
EP - 212
PY - 2021
DA - 2021/10
SN - 12
DO - http://doi.org/10.4208/eajam.100920.060121
UR - https://global-sci.org/intro/article_detail/eajam/19928.html
KW - Symmetry analysis, partial differential equations, the variable coefficients (2+1)-dimensional Bogoyavlensky-Konopelchenko equation.
AB - <p style="text-align: justify;">We present Lie symmetry analysis to explore solitary wave solutions, two-soliton type solutions and three-soliton type solutions in variable-coefficient nonlinear
physical phenomena. An example is a (2+1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko (VCBK) equation. We compute the Lie algebra of infinitesimals
of its symmetry vector fields and an optimal system of one-dimensional sub-Lie algebras
of the resulting symmetries. Two stages of Lie symmetry reductions will be built to
reduce the VCBK equation to nonlinear ordinary differential equations (ODEs) and new
analytical solutions to those ODEs will be found by using the integration method. Some
of such resulting solutions to the VCBK equation and their dynamics will be illustrated
through three-dimensional plots.</p>