Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation

Abstract

In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lump solutions of the Ito equation. In order to ensure rational localization and analyticity of these lump solutions, some sufficient and necessary conditions are provided on the parameters that appeared in the solutions. Furthermore, the interaction solutions between lump solutions and the stripe solitons are discussed by combining positive quadratic function with exponential function. Finally, the dynamic properties of these solutions are shown via the way of graphical analysis by selecting appropriate values of the parameters.

Elastic and nonelastic interactional solutions for the (2 + 1)-dimensional Ito equation

“…We note that the relations in Equation 7are the same as those in Yang et al (2017), Ma et al (2017), and Zou et al (2018). The Equation (8) indicates four cases…”

“…,, andZou et al (2018). If p ¼ 0 or q ¼ 0, the test function f is similar to that inTang et al (2016),Yang et al (2017), andMa et al (2017).…”

“…The breather-wave and the rational rogue wave solutions were provided in Wang, Tian, Qin, and Zhang (2017) with exp þ costype and exp-type test function. In Tang, Tao, and Guan (2016); Yang, Ma, and Qin (2017); Ma, Yong, and Zhang (2017); Zou, Yu, Tian, Feng, and Li (2018), the lump and the lump-soliton solutions were obtained with rational-type, rational þ exp-type and rational þ cosh-type test functions.…”

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

“…where D is a bilinear differential operator as follows [8]: [36], lump and lump-soliton solutions [37], interaction solutions between lump solutions and stripe solitons [38], rogue waves and multi-wave solutions [39], homoclinic breather waves [40]. In this paper, we will study other diverse exact analytical solutions of equation (6).…”

Localized interaction solutions of the (2+1)-dimensional Ito Equation

“…Very recently, it has also been shown that there are diverse interaction solutions to Eq. (1.1) [14,28] and even to linear equations [16] and there are abundant lump solutions to other nonlinear equations [13] [10] [11]. The framework of this paper is structured as follows.…”