Superposition solutions to a (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like equation

Abstract

In this paper, the superposition solutions of (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like(vcSTOL) equation are studied. The equation can illustrate various difficult sciences areas. Due to the wide application, it is very important to find the exact solutions of it. By introducing transformation, the equation is transformed into bilinear form. We use variable separation method and trial function method to obtain the superposition solutions of the equation containing different functions and forms. The images are drawn with the help of symbolic computing system Mathematica, and the properties of the solutions are analyzed. The analysis shows that different functions will affect the overall shape of waves, including the interaction between waves, the size, the direction and the number of waves, which can get more new phenomena. To our knowledge, those types of superposition solutions of (3+1)-dimensional vcSTOL equation mentioned in our work by variable separation method have not been reported before. Furthermore, we add the square terms to the expansion function, so that the obtained solutions have the characteristics of Lump solution, which has not been done in the previous literatures.

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

“…Using Hirota bilinear method [9][10][11] as a tool, the solutions of nonlinear evolution equations can be obtained. Besides, there are many methods to construct solutions of nonlinear evolution equations, such as backscattering method [12][13][14], Darboux transform method [15][16][17], variable separation method [18][19][20], Bäcklund transform method [21], auxiliary equation method [22][23][24][25][26] and so on.…”