She named the project after a sign she saw in the abode of Pope Celestine V, which translates as 'a room of one's own', and which Smith felt best described her solitary method of photography.
Finally, most of the solitary wave methods give only single solution, either of type soliton, singular-soliton, kink, singular-kink, periodic or singular-periodic.
Some of the methods are the inverse scattering method [1], the Hirota bilinear method [2, 3], the Bäklund transformation method [4 6], Darboux transformation [7, 8], the Painlevé analysis [9], the Lie group method [10 28], the solitary wave ansatz method [29 36], and others.
In addition, we note that the solitary wave ansatz method is an efficient method for constructing exact soliton solutions for nonlinear wave equations.
In this paper, the KS and JM equations are solved by the sine-cosine method as well as by the solitary wave ansatz method.
The solitary wave ansatz method is used to carry out the integration of these equations.
Since the functionals E ( u ) = ∫ − ∞ + ∞ [ 1 2 u L ( u ) − F ( u ) ] d x. and Q ( u ) = 1 2 ∫ − ∞ + ∞ u 2 d x. are two conserved quantities with (1.1), for studying the existence of solitary wave solutions to (1.1), by the variational methods, the solitary wave solutions to equation (1.1) will be founded as minimizers of.
In this present work, we have studied new extension of the (G′/G -expansion method for findinG′/G -expansionwave solutions of the methoded Korteweg–de Vries (mKdV) equation.
The study revealed a solitary ideal method for the keeper.
Diaz [7] analysed the solitary wave solution of the BHE through Cardano's method.
