Topological solitons and cnoidal waves to a few nonlinear wave equations in theoretical physics

Multi-dimensional nonlinear evolution equations are studied in this paper. Jacobi's elliptic function method, traveling wave hypothesis and Lie symmetry approaches are used to integrate these equations. The second approach only reveals toplogical 1-soliton solution while first approach displays an overwhelming number of solutions for these equations that include cnoidal waves, snoidal waves and others. In limiting cases, linear waves and solitary waves are revealed, depending on whether modulus of ellipticity approaches zero or one.