English abstract
We study analytical solutions of certain nonlinear evolution equations us ing Sine-Gordon equation expansion method, Sinh-Gordon equation expansion method and Tanh-Coth method. The Sine-Gordon equation expansion method has been used to obtain solutions of the generalized PHI-four equation, the gen eralized regularized long wave equation and modified Korteweg de Vries (mKDV) equation. We use the Sinh-Gordon equation expansion method to solve mKdV equation, Hamiltonian amplitude equation and a coupled wave equation. In this method, properties of Jacobi elliptic functions (JEFs) have been illustrated and solutions are obtained in terms of JEFs. The Tanh-Coth method has been em ployed to derive solutions of two types of Boussinesq equations, Sine-Gordon equation and the Liouville equation. The soliton solutions in terms of sech func tion, kink solutions in terms of odd powers of tanh function, singular solutions in terms of coth or csch functions and periodic solutions in terms of trigonometric functions have been derived for all equations under consideration.
