A generalized (2+1)-dimensional generalized KdV equation with a plethora of analytical solutions and conservation laws

A nonlinear evolution equation of the type u t + α u u x + u x x x + u x + ∫ − ∞ x u t y d x + u y + u x x y + β u u y + β u x ∫ − ∞ x u y d x = 0 , is a generalized (2+1) dimensional equation in which u = u ( x , y , t ) and α , β are real parameters. Together with an ansatz process and the multiple-exp function method, it will be examined from the perspective of Lie symmetry analysis. Lastly, conservation laws and their significant implications will be illustrated. To produce solitonic solutions, the multiple exp-function algorithm, a generalization of Hirota’s perturbation will be used.