Sine-Function Method In The Soliton Solution Of Nonlinear Partial Differential Equations

Abstract

In this paper we establish a traveling wave solution for nonlinear partial differential equations using sine-function method. The method is used to obtain the exact solutions for three different types of nonlinear partial differential equations like general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation(GKDV) which are the important soliton equations.

Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method

“…and the solitary wave equation of the modified equal width wave (MEWE) (Ali, Soliman, & Raslan, 2007;Evans & Raslan, 2005a, 2005bLu, Seadawy, & Ali, 2018;Rab & Akhter, 2013;Raslan, 2006Raslan, , 2008Raslan, Khalid, & Shallal, 2017) equation:…”

“…The Landau-Ginzburg-Higgs equation 1investigated through some methods, videlicet by the multi-symplectic Runge-Kutta method (Hu et al, 2009), the ðG 0 =G, 1=GÞ-expansion method (Iftikhar et al, 2013), the sine-cosine method and the extended tanh method (Cevikel et al, 2013), the first integral method (Bekir & Unsal, 2013), the new modified simple method (Irshad et al, 2017). And the solitary wave equation MEWE examined via some analytical schemes, as for instance the first integral method (Raslan, 2008), the sine-function method (Rab & Akhter, 2013), the extended simple equation method and the expðÀu n ð ÞÞ expansion method (Lu et al, 2018), the tanh function method (Evans & Raslan, 2005a), the collocation method using quadratic Bspline (Evans & Raslan, 2005b), the collocation method using cubic B-spline (Raslan, 2006), the modified extended tanh method (Raslan et al, 2017), Cosine-function method (Ali et al, 2007) etc. To our foremost understanding, the above stated equations have not been examined through the improved Bernoulli sub-equation function method (IBSEFM) (Aksan, Bulut, & Kayhan, 2017;Baskonus, Koc, & Bulut, 2016a, 2016bDusunceli, 2018Dusunceli, , 2019Yokus, Baskonus, Sulaiman, & Bulut, 2018).…”