Recently, the physics-informed neural networks (PINNs) have received more and more
attention because of their ability to solve nonlinear partial differential equations via only a …

In this research, based on Darboux transformation, a molecule consisting of two identical
soliton waves is firstly obtained by velocity resonance for modified KdV equation. And we …

Based on Darboux transformation, we generate breather solutions sitting on zero
background via module resonance for complex modified KdV equation. Then, some novel …

Based on velocity resonance and Darboux transformation, soliton molecules and hybrid
solutions consisting of soliton molecules and smooth positons are derived. Two new …

Dipolar interactions support the formation of intersite soliton molecules in a stack of quasi-
one-dimensional (quasi-1D) traps. We show that the stability and properties of individual …

Starting from a general sixth-order nonlinear wave equation, we present its multiple kink
solutions, which are related to the famous Hirota form. We also investigate the restrictions on …

Abstract We investigate a (3+ 1)-dimensional nonlinear evolution equation which is a higher-
dimensional generalization of the Korteweg–de Vries equation. On the basis of the …

The effect of dipolar orientation with respect to the soliton plane on the physics of two-
dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous …

In this paper, we investigate an extended complex modified Korteweg–de Vries equation.
On zero background, based on Darboux transformation, breather solutions, breather …

In this paper, we consider the integrable extended complex modified Korteweg–de Vries
equation. Based on Darboux transformation, we obtain soliton molecules, positon solutions …