We study the nonlinear waves on constant backgrounds of higher-order generalized Schrödinger (HGNLS) equation describing propagation ultrashort optical pulse in fibers. derive breather, rogue wave, and semirational solutions HGNLS equation. Our results show that these three types can be converted into nonpulsating soliton solutions. In particular, we present explicit conditions for transitions between breathers solitons with different structures. Further, investigate characteristics...

We study a variable-coefficient nonlinear Schr\"odinger (vc-NLS) equation with higher-order effects. show that the breather solution can be converted into four types of waves on constant backgrounds including multi-peak solitons, antidark soliton, periodic wave and W-shaped soliton. The transition condition requiring group velocity dispersion (GVD) third-order (TOD) to scale linearly is obtained analytically. display several kinds elastic interactions between transformed waves. discuss...

We study the higher-order generalized nonlinear Schrödinger (NLS) equation describing propagation of ultrashort optical pulse in fibres. By using Darboux transformation, we derive superregular breather solution that develops from a small localized perturbation. This type can be used to characterize stage modulation instability (MI) condensate. In particular, show some novel characteristics MI arising effects: (i) coexistence quasi-Akhmediev and multipeak soliton; (ii) two solitons opposite...

Three kinds of Darboux transformations are constructed by means the loop group method for complex reverse space-time (RST) nonlocal modified Korteweg–de Vries equation, which different from that PT symmetric (reverse space) and time models. The N-periodic, N-soliton, N-breather-like solutions, are, respectively, associated with real, pure imaginary, general eigenvalues on a finite background presented in compact determinant forms. Some typical localized wave patterns such as doubly periodic...

In this paper, we study the modulations of nonlinear transformed waves for a (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluids or plasma. By virtue phase shift analysis, shape-changed and unchanged are investigated, which shows inhomogeneity can restrain time-varying property. The deformation is determined by difference between two wave components. addition, evolutions parabolic illustrated via characteristic lines analysis. interactions further explored,...

The very fast transient overvoltage (VFTO) generated during switching of the disconnector (DS) in gas-insulated switchgear (GIS) may threaten insulation electrical equipment. DS characteristics are important influence factors for VFTO. To study on VFTO GIS, an experimental was conducted two established full-scale 1100-kV GIS test circuits. More than 1800 tests circuits were carried out. In one circuit, effect operating speed amplitude and trapped charge voltage studied by changing DS....

To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on three-component Gross-Pitaevskii (GP) equations. Via Darboux-dressing transformation, obtain a family rational solutions describing extreme events, i.e. waves. This includes bright-dark-bright bright-bright-bright The algebraic construction depends Lax matrices their Jordan form. conditions for wave BEC are discussed. For GP equations, if there is modulation instability, it...

Under investigation in this paper, with symbolic computation, is a variable-coefficient variant Boussinesq (vcvB) model for the nonlinear and dispersive long gravity waves travelling two horizontal directions varying depth. Connection between vcvB Broer-Kaup (vcBK) system revealed under certain constraints. By means of N -fold Darboux transformation vcBK system, odd-soliton-like solutions terms Vandermonde-like determinant are derived. Dynamics those analyzed graphically, on three-parallel...

In the paper, we employ an improved physics-informed neural network (PINN) algorithm to investigate data-driven nonlinear wave solutions nonlocal Davey–Stewartson (DS) I equation with parity-time (PT) symmetry, including line breather, kink-shaped and W-shaped rogue solutions. Both PT symmetry model are introduced into loss function strengthen physical constraint. addition, since DS is a high-dimensional coupled system, this leads increase in number of output results. The also needs be...

This paper is to investigate the extended (2+1)-dimensional Konopelchenko—Dubrovsky equations, which can be applied describing certain phenomena in stratified shear flow, internal and shallow-water waves, plasmas other fields. Painlevé analysis passed through via symbolic computation. Bilinear-form equations are constructed soliton solutions derived. Soliton interactions illustrated. Bäcklund transformation a type of obtained.

Abstract The nonlinear wave molecules of the Lakshmanan–Porsezian–Daniel (LPD) equation describing propagation ultrashort optical pulses through fibers and Davydov soliton in α‐helical proteins are investigated. Based on analysis characteristic lines, breather consisting two, three, or even four different atoms derived, synthesis modes by adjusting values phase parameters generated. state conversion is studied a variety converted produced. In particular, it reported that full does not exist...

Under investigation in this paper is a variable-coefficient AB (vcAB) system, which describes marginally unstable baroclinic wave packets geophysical fluids and ultra-short pulses nonlinear optics. The modulation instability analysis of solutions with variable coefficients the presence small perturbation studied. modified Darboux transformation (mDT) vcAB system constructed via gauge transformation. first-order non-autonomous rogue are presented based on mDT. It found that amplitude...