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In this research communication the Boussinesq like equation namely 2 + 1 − dimensional Wazwaz Kaur Boussinesq equation is studied and gotten their Jacobi elliptic function (doubly periodic) solutions employing the simple algebraic Jacobi elliptic function method. The said method makes the two transformations of nonlinear partial differential equations to ordinary differential equations to solvable system of algebraic equations. The gotten doubly periodic solutions are modular transformed to show the degeneration into non-topological solitons, compound non-topological singular solitons and complex singular solitons. The three dimensional surfaces are drawn for few elliptic solutions and solitons. • The (2+1) dimensional Wazwaz Kaur Boussinesq equation is studied. • By employing Jacobi elliptic function method doubly periodic solutions are obtained. • The degeneration of Jacobi elliptic solutions to non-topological soliton is shown. [ABSTRACT FROM AUTHOR]