Abstract
AbstractThe invariant solutions of generalised modified \(\alpha \) equation are obtained by using the Lie classical symmetry method. The obtained solutions are in terms of trigonometric functions and hyperbolic functions. This equation can be used in solidifying and nucleation problem. The conservation laws are obtained by using the multiplier approach. The graphical representations are also shown for some of the obtained solutions. Some new solutions of those equations are found that have been considered earlier in literature, as well as some of the previous solutions can also be recovered by taking particular values.KeywordsModified \(\alpha \) equationLie classical methodInfinitesimalsInvariant solutionsSolitonsConservation lawsMathematics Subject Classification (2010)35B0635B1035C0735C0935C1135G20
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