Abstract
The current study deals with investigation of various lumps, breathers and interaction solutions to the (1 + 1) -dimensional longitudinal wave equation in magneto electro-elastic circular rod via bilinear method and choosing appropriate polynomial function. In particular, we obtain lump, interaction of lump with one kink, interaction of lump with two kink, lump periodic, Manifold periodic, Ma breather, Kuznetsov-Ma breather and its corresponding rogue wave solutions for ensuing model. The Cole-Hopf transformation is implemented on the stated equation to produce its bilinear form. By choosing the function f in bilinear form of the (1 + 1) -dimensional longitudinal wave equation as the positive quadratic polynomial function, a kind of lump type solution which involves eleven parameters with six arbitrary independent parameters is obtained. We also obtain rogue wave solutions formed by the interaction of lump solution and a pair of stripe solitons. Furthermore, the dynamics of these solutions are figured out graphically by choosing suitable values to parameters.