Analytical solutions of conformable Drinfel’d–Sokolov–Wilson and Boiti Leon Pempinelli equations via sine–cosine method

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

“…[40], we obtain the solutions to Eq. ( 18) as sinh w(η) = ±csch(η) or cosh w(η) = ± coth(η), (19) sinh w(η) = ±i sech(η) or cosh w(η) = ± tanh(η), (20) here i 2 = −1.…”

“…Step 5 From the gained results, i.e., Eqs. (19) and (20), we obtain the analytical wave solutions to Eq. ( 15) as follows:…”

“…[11] Similarly, Hirota bilinear method, [12] modified extended tanh expansion method, [13] modified simplest equation technique, [14] extended Jacobi elliptic function scheme, [15] sech and tanh function solutions are obtained by using the sine-Gordon expansion scheme, [16] sinh, cosh, sin and cos involving solutions are gained by utilizing the rational sine-Gordon expansion technique [17] and many other techniques. [18][19][20][21][22][23][24] In this study, we use two schemes, i.e., the exp a function and extended sinh-Gordon equation expansion (EShGEE) schemes. The general exp a function scheme was first proposed by Ali and Hassan in Ref.…”

Exact solutions and bifurcations of the time-fractional coupled Boussinesq-Burgers equation

“…The study of exact solutions of NFPDEs facilitates researchers to drill deeper into the physical interpretation of the solutions. For now, a large number of effective and practical methods have been applied to explore exact solutions of NFPDEs, such as the modified extended tanh-function (mETF for short) method [1,2], the improved ( ) ¢ G G method [3, 4], the two variables ( ) ¢ G G G , 1 -expansion method [5][6][7], the Darboux transformation method [8], the Kudryashov method [9,10], the exp-function method [11,12], the Hirota's bilinear method [13], the first integral method [14], the sine-cosine method [15,16], the modified ( ) ¢ G G 2 -expansion method [17][18][19] and the Bifurcation method [20][21][22], and so on [23][24][25].…”

Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle

“…In addition, several studies show that interaction solutions between lumps and other types of solutions to nonlinear integrable equations existed. It should be emphasized, however, that numerous approaches such as the Lie symmetric analysis and its application [9][10][11][12][13][14], the Kudryashov method [15,16], the tanhcoth method [17], the improved Sardar-subequation [18], the new generalized auxiliary equation method [19], and other techniques [20][21][22][23][24] have been employed for generating interaction phenomena for nonlinear differential equations. Values are assigned to these constant coefficients in particular conditions to ensure that solutions exist [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”