Constructing rogue wave prototypes of nonlinear evolution equations via an extended tanh method

Rational Solutions and Their Interaction Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

“…Step 3. By substituting (16) and 17into Equation 13 where other parameters in Cases 1-3 are arbitrary real constants.…”

“…Step 4. By substituting a 0 , a ij in Cases 1-3 into (16) and 17and using transformation (9), we obtain the following highorder lump-type solutions for Jimbo-Miwa equation (8).…”

“…Remark 6. By substituting a 0 , a ij in Cases 4-7 to (16) and (17) and using bilinear transformation (9), we obtain the new lump solutions for Jimbo-Miwa equation (8). Due to the lack of space, we omit the expressions of lump solutions.…”

“…In the recent decade, several direct methods for finding the exact solutions to NLEEs have been proposed [1][2][3][4][5][6][7][8][9]. Thousands of examples have shown that these methods are powerful for obtaining exact solutions of NLEEs, such as soliton [10][11][12][13][14], rogue wave [15,16], breather solution [17], periodic wave solution [18][19][20][21], and optical solution [22,23].…”

Diversity of New Three-Wave Solutions and New Periodic Waves for the (3 + 1)-Dimensional Kadomtsev-Petviashvili-Boussinesq-Like Equation

“…The Hirota bilinear form plays an important role in presenting soliton solutions, although some intelligent guessing is usually required. In recent years, more ex-act solutions have been found for solving integrable equations, such as solitary wave [2] [3] [4] [5] [6], rogue waves [7] [8] [9], periodic solitary wave [10] [11] [12], optical soliton [13], lump solution and interaction solution [14]- [34], and cross-kink wave solution [35]. It is natural and interesting to search for new three-wave solutions and new periodic wave to NPDEs taking advantage of hirota bilinear forms.…”