Soliton Dynamics of the Generalized Shallow Water Like Equation in Nonlinear Phenomenon
Ghazala Akram, Maasoomah Sadaf, M. Atta Ullah Khan
Abstract
The generalized shallow water like equation is investigated in this research paper. Exact solutions of generalized shallow water like equation are extracted using modified auxiliary equation (MAE) method and extended <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> -expansion method. Many novel soliton solutions are obtained using these methods. The retrieved solution of governing model include rational, trigonometric and hyperbolic functions. The 3D graphs, 2D contour graphs and line graphs of obtained solutions are plotted using symbolic software such as Maple. The aim of plotting graphs is to demonstrate the dynamical behavior of acquired solutions. Thus, this study investigate the exact soliton solutions of generalized shallow water like using proposed methods.