On Lie symmetries and invariant solutions of (2+1)-dimensional Gardner equation

The present article is devoted to obtain some invariant solutions of (2+1)-dimensional Gardner equation by using similarity transformation method. The equation describes directional wave trains with larger spreading angles and more nonlinear waves than KP equation due to its cubic term. All the symmetry reduction and possible vector fields have been obtained by using invariance property of Lie group theory. The method reduces the number of independent variables by one. Thus, Gardner equation is reduced into a system of ordinary differential equations, which is solved under adequate parametric restrictions. The obtained results are more significant and helpful to explain physical phenomena due to existence of various arbitrary constants and function. The results are analyzed physically on the basis of numerical simulation. Consequently, the elastic behavior of multisoliton, positon, kink waves, soliton fusion and stationary profiles of the results are shown in the analysis and discussions section to make this research more worthy.