On the Lie Symmetry Analysis of the Generalized Seventh-Order Nonlinear Kawahara Equation
DOI:
https://doi.org/10.24297/qrnybf21Keywords:
exact power series solutions, invariant solutions, similarity reduction, symmetry reduction, prolongations, Lie symmetry analysis, Kawahara equationAbstract
In this paper, a comprehensive Lie symmetry analysis of the generalized seventh-order Kawahara equation is carried out. The equation considered is ut+6uux+uxxx-uxxxxx+βuxxxxxxx=0,β0 where u=u(x,t)and is a non-zero constant parameter. The study systematically determines the total derivative operators and constructs the seventh prolongation of the infinitesimal generator. The invariance condition is applied to obtain the determining equations, which yield a three-dimensional Lie algebra of infinitesimal symmetries.
Optimal systems of one-dimensional subalgebras are derived and used to obtain similarity variables and invariant reductions. The reduced ordinary differential equations are analyzed to construct exact invariant solutions, including solitary wave structures. Furthermore, exact power series solutions are derived via recursive coefficient relations. The results provide deeper insight into the symmetry structure, integrability properties, and nonlinear wave behavior governed by higher-order dispersive systems.
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Copyright (c) 2026 Winny Chepngetich, Owino M. Oduor, Joshua K. Limo
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