Mathematics and Statistics Vol. 7(1), pp. 10 - 13
DOI: 10.13189/ms.2019.070102
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Exact Traveling Wave Solutions of Nonlinear Evolution Equations: Indeterminant Homogeneous Balance and Linearizability

Barbara Abraham-Shrauner ^*
Department of Electrical and Systems Engineering, Washington University, USA

ABSTRACT

Exact traveling (solitary) wave solutions of nonlinear partial differential equations (NLPDEs) are analyzed for third-order nonlinear evolution equations. These equations have indeterminant homogenous balance and therefore cannot be solved by the Power Index Method (PIM). Some evolution equations are linearizable where solutions are transferred from those of a linear PDE. For other evolution equations transforming to a NLPDE which has a homogenous balance gives rise to possible solutions by the PIM. The solutions for evolution equations that are not linearizable are developed here.

KEYWORDS
Evolution Equations, Homogeneous Balance, Traveling Waves, Lie Symmetry, PIM

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Barbara Abraham-Shrauner , "Exact Traveling Wave Solutions of Nonlinear Evolution Equations: Indeterminant Homogeneous Balance and Linearizability," Mathematics and Statistics, Vol. 7, No. 1, pp. 10 - 13, 2019. DOI: 10.13189/ms.2019.070102.

(b). APA Format:
Barbara Abraham-Shrauner (2019). Exact Traveling Wave Solutions of Nonlinear Evolution Equations: Indeterminant Homogeneous Balance and Linearizability. Mathematics and Statistics, 7(1), 10 - 13. DOI: 10.13189/ms.2019.070102.