Abstract
The local modified $$\exp (-\Omega (\eta ))$$ -expansion function method is proposed to construct analytical solutions of nonlinear local partial differential equations, involving local M-derivative of order $$\alpha$$ . The modified $$\exp (-\Omega (\eta ))$$ -expansion function method is applied to obtain some solitary wave solutions to the longitudinal wave equation in a magneto electro-elastic circular rod. Some soliton solutions are constructed under some constraint conditions.
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