Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics

Decay mode solutions to cylindrical KP equation

“…Considering the homogeneous balance between , according to the SHB [8] , which means that an undetermined function ( F φ ) and its partial derivatives x F = ' x F φ …, that appearing in the original homogeneous balance (BH) [9][10][11][12] …”

“…(1) can be obtained by Backlund transformation and Hirota's method. In this paper, we will use the simplified homogeneous balance method(SHB) [8][9][10][11][12] to derive a nonlinear transformation for the CKP equation, based on the transformation derived here, the 1-decay mode and 2-decay mode solutions of CKP equation can be obtained. These results are different form those obtained in the previous literatures.…”

Exact traveling wave solutions of some nonlinear evolution equations

“…Exact solutions to nonlinear partial differential equations play an important role in nonlinear physical science since they can provide much physical information and more insight into the physical aspects of the problem and thus lead to further applications. In recent years, many methods for obtaining explicit traveling and solitary wave solutions of NLEEs have been proposed such as inverse scattering transform method [2], Darboux transformation method [3,4], Hirota's bilinear method [5], Bäcklund transformation method [6], homogeneous balance method [7], solitary wave ansatz method [8,9], Jacobi elliptic function expansion method [10], the tanh function method [11], ð G 0 G Þ expansion method [12,13], F-expansion method [14], projective Ricatti equation method [15,16,17] and so on. Among them extended F-expansion and projective Ricatti equation methods have been proved to be a powerful mathematical tool to investigate the exact solutions for NLEEs.…”

Propagation of Dark Solitary Waves in the Korteveg-Devries-Burgers Equation Describing the Nonlinear RLC Transmission

“…So, finding exact solutions is important to understand the mechanism of the complicated nonlinear physical phenomena. In the recent decade, several methods for finding the exact solutions to nonlinear equations of mathematical physics have been proposed, such as trigonometric function series method [12], the modified mapping method and the extended mapping method [13] [14], homogeneous balance method [15], tanh function method [16], extended tanh function method [17], hyperbolic function method [18], rational expansion method [19], sine-cosine method [20], Jacobi elliptic function method [21], F-expansion method [22], and so on. Our goal is to present a method to computational study of solitary waves in nonlinear RLC transmission lines.…”