Solutions of the nonlinear Schrödinger equation, appearing as rogue waves on a spatially-
periodic background envelope, are obtained using the Darboux transformation scheme …

We construct and discuss a semirational, multiparametric vector solution of coupled
nonlinear Schrödinger equations (Manakov system). This family of solutions includes known …

This review is dedicated to recent progress in the active field of rogue waves, with an
emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector …

In this paper, we focus on the interaction behavior associated with a generalized (2+ 1)-
dimensional Hirota bilinear equation. With symbolic computation, two types of interaction …

In this paper, using the Darboux transformation, we demonstrate the generation of first-order
breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation …

Abstract The cylindrical Kadomtsev-Petviashvili (cKP) equation related to cylindrical
geometry, as one type of the variable-coefficient KP equation, is widely used to describe …

Abstract The (3+ 1)-dimensional generalized shallow water wave equation is systematically
investigated in this paper based on the Hirota bilinear method. The N-soliton solution and …

Understanding the phenomenon of rogue wave formation, often called extreme waves, in
diverse branches of nonlinear science has become one of the most attractive domains …

Water waves are one of the most common phenomena in nature, the study of which helps in
designing the related industries. In this paper, a generalized (3+ 1 3+ 1)-dimensional B-type …

An improved physics-informed neural network (IPINN) algorithm with four output functions
and four physics constraints, which possesses neuron-wise locally adaptive activation …