TY - JOUR
ID - 16921
TI - Lie symmetry analysis for computing invariant manifolds associated with equilibrium solutions
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Dehghan Nezhad, Akbar
AU - Moghaddam Zeabadi, Mina
AD - School of Mathematics and Computer Science, Iran University of Science and Technology,
Narmak, Tehran, Iran.
Y1 - 2024
PY - 2024
VL - 12
IS - 2
SP - 266
EP - 286
KW - Lie symmetry analysis
KW - Parameterization method
KW - Equilibrium solution
KW - Eigenvalue problem
KW - Invariant manifolds
KW - Invariance equation
KW - tanh method
DO - 10.22034/cmde.2023.54283.2268
N2 - We present a novel computational approach for computing invariant manifolds that correspond to equilibrium solutions of nonlinear parabolic partial differential equations (or PDEs). Our computational method combines Lie symmetry analysis with the parameterization method. The equilibrium solutions of PDEs and the solutions of eigenvalue problems are exactly obtained. As the linearization of the studied nonlinear PDEs at equilibrium solutions yields zero eigenvalues, these solutions are non-hyperbolic, and some invariant manifolds are center manifolds. We use the parameterization method to model the infinitesimal invariance equations that parameterize the invariant manifolds. We utilize Lie symmetry analysis to solve the invariance equations. We apply our framework to investigate the Fisher equation and the Brain Tumor growth differential equation.
UR - https://cmde.tabrizu.ac.ir/article_16921.html
L1 - https://cmde.tabrizu.ac.ir/article_16921_27fa5a1ef04691fef4b60494658a6f54.pdf
ER -