Solitary and Rogue Wave Solutions to the Conformable Time Fractional Modified Kawahara Equation in Mathematical Physics
Nur Hasan Mahmud Shahen, Foyjonnesa, Md. Habibul Bashar, Tasnim Tahseen, S. Hossain
Abstract
Utilizing of illustrative scheming programming, the study inspects the careful voyaging wave engagements from the nonlinear time fractional modified Kawahara equation (mKE) by employing the advanced <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi mathvariant="normal">exp</a:mi> <a:mfenced open="(" close=")"> <a:mrow> <a:mo>−</a:mo> <a:mi>φ</a:mi> <a:mfenced open="(" close=")"> <a:mrow> <a:mi>ξ</a:mi> </a:mrow> </a:mfenced> </a:mrow> </a:mfenced> </a:math> -expansion policy in terms of trigonometric, hyperbolic, and rational function through some treasured fractional order derivative and free parameters. The undercurrents of nonlinear wave answer are scrutinized and confirmed by MATLAB in 3D and 2D plots, and density plot by specific values of the convoluted parameters is designed. Our preferred advanced <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M2"> <h:mi mathvariant="normal">exp</h:mi> <h:mfenced open="(" close=")"> <h:mrow> <h:mo>−</h:mo> <h:mi>φ</h:mi> <h:mfenced open="(" close=")"> <h:mrow> <h:mi>ξ</h:mi> </h:mrow> </h:mfenced> </h:mrow> </h:mfenced> </h:math> -expansion technique which is parallel to ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M3"> <o:msup> <o:mrow> <o:mi>G</o:mi> </o:mrow> <o:mrow> <o:mo>′</o:mo> </o:mrow> </o:msup> <o:mo>/</o:mo> <o:mi>G</o:mi> </o:math> ) expansion technique is trustworthy dealing for searching significant nonlinear waves that progress a modification of dynamic depictions that ascend in mathematical physics and engineering grounds.