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Vol.1, 2011
Traveling wave, lump wave, rogue wave, multi-Kink solitary wave and interaction solutions
Shou-Fu Tian,Ding Guo,Xiu-Bin Wang,Tian-Tian Zhang
Keywords:The (3+1)-dimensional Kadomtsev-Petviashvili equation, Traveling wave solution, Lump solutions, interaction solution, Rogue wave solution, Multi-kink solitary wave solution
      We consider a (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation. By using the Hirota bilinear operators, we construct the bilinear form of the equation. Based on the resulting bilinear form, we further derive the B\"{a}cklund transformation and the traveling wave solutions of the equation. Furthermore, lump solutions are constructed by searching the positive function from the Hirota bilinear formalism. Meanwhile, we also obtain the interaction solutions between lump solutions and the stripe solitons. We discuss the influences of each parameters on these exact solutions by using several graphics. Finally, we successfully construct its rogue wave solutions and multi-kink solitary wave solutions. It is hoped that our results can be used to enrich the dynamical behavior of the (3+1)-dimensional KP-type equations.