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Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized ‐expansion method
Author(s) -
Kaur Lakhveer,
Gupta R. K.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2617
Subject(s) - mathematics , hyperbolic function , homogeneous space , trigonometric functions , mathematical analysis , function (biology) , variable (mathematics) , series (stratigraphy) , power series , symmetry (geometry) , similarity (geometry) , geometry , paleontology , evolutionary biology , biology , artificial intelligence , computer science , image (mathematics)
In this paper, variable coefficients Kawahara equation (VCKE) and variable coefficients modified Kawahara equation (VCMKE), which arise in modeling of various physical phenomena, are studied by Lie group analysis. The similarity reductions and exact solutions are derived by determining the complete sets of point symmetries of these equations. Moreover, some exact analytic solutions are considered by the power series method. Further, a generalized ‐expansion method is applied to VCKE and VCMKE for constructing some new exact solutions. As a result, hyperbolic function solutions, trigonometric function solutions and some rational function solutions with parameters are furnished. Copyright © 2012 John Wiley & Sons, Ltd.