New Traveling Wave Solutions to the Vakhnenko-Parkes Equation

Abstract

We apply the improved (G′/G) expansion method to the Vakhnenko-Parkes equation. As a result, many new and more general exact solutions have been obtained for the equation. Comparing our solutions with those gained by other authors indicates that the improved (G′/G) expansion is more effective in solving the general solutions to differential equations.

Transmission of high-frequency waves in a tranquil medium with general form of the Vakhnenko dynamical equation

“…,B 3 =0, then we have, 20) in [51]. The remnant all solutions are novel and having fruitful application in applied science.…”

“…This equation is provides a rich platform for the description of the transmission of high-frequency waves in a tranquil medium and also having fruitful pplications in nonlinear science [50,51]. Consider the new independent variable X,T define by…”

“…Several distinct methodologies were employed for determination analytical solution of this equation. But here in this segment, we will comparison our results with derived solutions in[49][50][51]. By choosing the different values of B N in equation (4) and a i , b i in equation (5), obtained many solutions.…”

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(−ϕ(ξ))-expansion method

“…The traveling wave solutions of this Vakhnenko-Parkes equation was investigated in (Kangalgil and Ayaz 2008 ; Parkes 2010b ; Gandarias and Bruzon 2009 ; Yasar 2010 ; Abazari 2010 ; Liu and He 2013 , Ostrovsky 1978 ) and Liu (Liu and He 2013 ) found traveling wave solutions of this equations by improved ( G ′/ G ) -expansion method with auxiliary equation GG ″ = AG 2 + BGG ′ + C ( G ′) 2 .…”

Traveling Wave Solution of Vakhnenko-Parkes Equation

“…Many scientists have been studied with (V-P) equation. Some of these are as follows: solutions of the (V-P) equation are obtained using the inverse scattering method Vakhnenko and Parkes (2012), with the help of exp-function and the exp-(− ( ))expansion method, the exact solutions of the (V-P) equation are obtained Roshid et al (2014), two solitary wave solutions of (V-P) equation are attained using the ansatz method Majid et al (2012), different type solutions of (V-P) equation are attained Ye et al (2012), analytic solutions to the (V-P) equation using the complex method Gu et al (2017), exact solutions of the (V-P) equation are obtained using the improved   G' G expansion method Liu and He (2013), different type solutions of the (V-P) equation are obtained with the aim of the Bernoulli sub-equation function method (Baskonus et al,2015).…”