Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

“…Step v: Solve the set of algebraic equations, which may not be consistent to derive solitary wave solutions and doubly periodic solutions of the given nonlinear equations using (2) It is easy to see that the solutions derived from the above-mentioned method include both the results of the sine-cosine method [4][5][6], the Riccati method [10][11][12], the Fu's method [7], the sinh-Gordon equation expansion method [13], the algebraic method without Weierstrass elliptic function solutions [14], the projective Riccati equation method [15,16] and the sn-and cn-function method [17] and new solutions.…”

Solitary wave solutions of two KdV-type equations

“…Thereafter, many studies have been carried out to generalise the projective Riccati equation method and to obtain a variety of exact solutions to nonlinear partial diffrenetial equations. For more details, see [33][34][35][36][37][38]. Recently, Kumar and Chand [39] have examined the exact traveling wave solutions of some nonlinear evolution equations.…”

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(<i>ξ</i>))-Expansion Method

“…Therefore, it is necessary to solve them analytically or numerically. Some of the methods to solve them analytically are the Hirota method [1], the projective Riccati equation method [2], the homogeneous balance method [3]- [5], the tanh-function method [6]- [10], the exp-function method [11], the improved F-expansion method [12], the ( ) ( ) exp ξ −Φ -expansion method [13]- [19], sine-cosine method [20], the modified simple equation method [21], the ( ) G G ′ -expansion method [22] [23], the modified extended tanh-function method with Riccati equation [24] and others. In the references [13]- …”