Diverse exact analytical solutions and novel interaction solutions for the (2+1)-dimensional Ito equation

Abstract

In this paper, we studied a novel form of exact analytical solutions of (2+1)-dimensional Ito equation based on Hirota bilinear method. By using symbolic computation, assorted exact analytical solutions including high-order rational solutions, three-wave solutions, breather solutions and interaction solutions between the above solutions were obtained through choosing the order of terms as well as different basic functions. The exact solutions of (2+1)-dimensional Ito equation on current literatures are extremely enriched. Furthermore, both three-dimensional plots and corresponding contour maps with different determinant values vividly show the movement of waves and the collision phenomena.

High-order localized waves in the (2+1)-dimensional Ito equation

“…In addition, according to the time delay effect caused by the phase factor, we analyze the interaction of a line soliton and a lump-type localized wave, which can be divided into two categories: absorb-emit and emit-absorb interactions. Compared with the former work in the (2+1)-dimensional Ito equation [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], some novel highorder localized wave solutions and interesting dynamics characteristics are presented.…”

“…In particular, if ò = 0, then the generalized bilinear differential equation (2.3) reduces to (1.7). Hence the bilinear differential equation (2.3) is a generalization form of (1.7) and has not been considered in the former work [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Next, based on the generalized bilinear differential equation (2.3), we will investigate different types of high-order localized waves in the (2+1)-dimensional Ito equation.…”

“…which is referred to as the (2+1)-dimensional Ito equation [18][19][20][21][22][23][24][25][26][27][28][29][30][31], where u = u(x, y, t) is a real differentiable function, x and y denote the spatial variables, the variable t denotes time. The parameters α and β are real constants.…”

“…Ma and his collaborators investigated the interaction phenomena between lump solutions and other localized waves [24][25][26]. Recently, Feng derived some analytical solutions and interaction solutions by means of different test functions [27]. Wang discussed and presented the state transition of rogue waves and breathers [28].…”

Dynamics of kink-soliton solutions for $2+1$-dimensional sine-Gordon equation

“…al [29] have derived 2D SGE from the AKNS system and obtained nontrivial explicit solutions. The 2D integrable equations have studied recent years [30,31,32,33]. As we have already mentioned above that the integrable 1D SGE explains different physical phenomenon, including the propagation of fluxons in a junction between two superconductors (also known as Josephson junction), the motion of coupled pendulum, dislocations in crystals and dynamics of DNA (Deoxyribonucleic acid).…”