Exact solutions to the combined KdV–mKdV equation by the extended mapping method

Abstract

The extended mapping method has been used to derive some new exact solutions of the KdV-mKdV equation as a combination of some Jacobian elliptic functions. Solutions in the limiting cases have also been studied.

Exact solutions of KdV equation with time-dependent coefficients

“…Lot of studies have been conducted with this equation [1][2][3][4][5][6][7]. Some of them are the integrability aspects, soliton perturbation theory, quasi-stationarity, quasi-particle theory, stochasticity and many more.…”

Solutions of the fractional combined KdV–mKdV equation with collocation method using radial basis function and their geometrical obstructions

“…[22][23][24][25][26][27][28][29][30] etc.). The combined KdV-mKdV equation is one of the most popular equations in soliton physics and wave propagation of bound particle.…”

New interaction solutions to the combined KdV–mKdV equation from CTE method

“…(1) have been studied by means of the extended mapping method, extended tanh expansion method and new Riccati equation expansion method (Bekir, 2009;Huang andZhang, 2006 Sirendaoerji, 2006;Zhao et al, 2006). The generalization form in (2+1)-dimensions of the combined KdV-mKdV equation has been discussed in Dai and Wang (2014), Geng and Cao (2001), Krishnan and Peng (2006), Zhang and Lin (1995), and Zhou and Ma (2000). The paper is organized as follows.…”