Extended Jacobi elliptic function solutions for general boussinesq systems

Abstract

In this research paper, we have utilized the Jacobi elliptic function expansion method to obtain the exact solutions of (1+1)- dimensional Boussinesq System (GBQS). The most important difference that distinguishes this method from other methods is the parameters included in the auxiliary equation F’ (ξ) = Ö P F4(ξ) + QF2(ξ) + R. As far as the authors know, there is no other study in which such a variety of solutions has been given. Depending on P, Q and R, nineteen the solitary wave and periodic wave solutions are obtained at their limit conditions. In addition, 3D and contour plot graphics for the constructed waves are investigated with the computer package program by giving special values to the parameters involved. The validity and reliability of the method is examined by its applications on a class of nonlinear evolution equations of special interest in nonlinear mathematical physics. The results were acquired to verify that the recommended method is applicable and reliable for the analytic treatment of a wide application of nonlinear phenomena

Retracted: Exploring new optical solutions for nonlinear Hamiltonian amplitude equation via two integration schemes

“…Jacobi elliptic functions have numerous applications in mathematical physics, including in the theory of elliptic integrals, the study of periodic solutions of nonlinear differential equations, and the analysis of periodic structures in materials science. The Jacobi elliptic function expansion method has been applied to a wide range of nonlinear partial differential equations [29][30][31][32][33][34][35][36][37][38]. The fundamental outline of JEFEM can be summarized as follows:…”

“…expansion method [11,12], the Bernoulli subequation function method [13], the generalized exponential rational function method [14-16], the ¢ -( ) G 1 expansion method [17, 18], Hirota's simple method [19][20][21], and other methods [22][23][24][25][26][27] have been used to obtain solutions for these NPDEs. Additionally, the Jacobi elliptic function expansion method (JEFEM) has been applied to several NPDEs, including the Biswas-Arshed equation in [28], various nonlinear wave equations such as KdV, mKdV equations, Boussinesq model and nonlinear klein-gordon equation [29], the fourth-order NPDE and the Kaup-Newell equation in [30], and other related studies [31][32][33][34][35][36][37][38].Similarly, the new modification of the Sardar sub-equation method (MSSEM) has also been applied to several NPDEs such as the generalized unstable nonlinear Schrodinger equation in [39], the perturbed Fokas-Lenells equation in [40], the Korteweg-de Vries equation in [41], the Benjamin-Bona-Mahony equation and the Klein-Gordon equations in [42], the Klein-Fock-Gordon equation in [43], the Boussinesq equation in [44], the perturbed Gerdjikov-Ivanov equation in [45], and other related studies [46][47][48][49][50][51][52].…”

Exact Traveling Wave Solutions for the Non-Linear Couple Drinfel’d-Sokolov-Wilson (Dsw) Dynamical System Using Extended Jacobi Elliptic Function Expansion Method

“…There are many methods in the literature to obtain wave solutions of partial differential equations. Some of these are the F-expansion method [4], the Jacobi elliptic function expansion method [5,6], (G'/G)-expansion method [7], Lie symmetry approach [8], and so on [9][10][11][12].…”