Spatiotemporal vector and scalar solitons of the coupled nonlinear Schrödinger equation with spatially modulated cubic–quintic–septimal nonlinearities

Nonlinear Dynamics - The spatially modulated cubic–quintic–septimal nonlinearities and transverse modulation are introduced to study the impact on a...     

Scalar and vector multipole and vortex solitons in the spatially modulated cubic–quintic nonlinear media

We derive scalar and vector multipole and vortex soliton solutions in the spatially modulated cubic–quintic nonlinear media, which is governed by a (3+1)-dimensional N-coupled cubic–quintic nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation. If the modulation depth \(q=1\), the vortex soliton is constructed, and if \(q=0\), the multipole soliton, including dipole, quadrupole, hexapole, octopole and dodecagon solitons, is constructed, respectively, when the topological charge \(k=1\)–5. If the topological charge \(k=0\), scalar solitons can be obtained. Moreover, the number of layers for the scalar and vector multipole and vortex solitons is decided by the value of the soliton order number n.     

Dynamics of superregular breathers in the quintic nonlinear Schrödinger equation

In this paper, we consider an extended nonlinear Schrödinger equation that includes fifth-order dispersion with matching higher-order nonlinear terms. Via the modified Darboux transformation and Joukowsky transform, we present the superregular breather (SRB), multipeak soliton and hybrid solutions. The latter two modes appear as a result of the higher-order effects and are converted from a SRB one, which cannot exist for the standard NLS equation. These solutions reduce to a small localized perturbation of the background at time zero, which is different from the previous analytical solutions. The corresponding state transition conditions are given analytically. The relationship between modulation instability and state transition is unveiled. Our results will enrich the dynamics of nonlinear waves in a higher-order wave system.     

Equivalence transformations and differential invariants of a generalized cubic–quintic nonlinear Schrödinger equation with variable coefficients

Nonlinear Dynamics - In this paper, a variable-coefficient cubic–quintic nonlinear Schrödinger equation involving five arbitrary real functions of space and time is analyzed from the...     

Breathers,solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds

Nonlinear Dynamics - We investigate the generation of breathers, solitons, and rogue waves of the quintic nonlinear Schrödinger equation (QNLSE) on uniform and elliptical backgrounds. The...     

Dynamics of solitons in the fourth-order nonlocal nonlinear Schrödinger equation

Nonlinear Dynamics - We consider the fourth-order nonlocal nonlinear Schrödinger equation and generate the Lax pair. We then employ Darboux transformation to generate dark and antidark soliton...     

Bright soliton solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing term

Nonlinear Dynamics - The (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing (FWM) term is studied in this paper, which describes the optical...     

Bright–dark solitons in the space-shifted nonlocal coupled nonlinear Schrödinger equation

Nonlinear Dynamics - Multiple bright–dark soliton solutions in terms of determinants for the space-shifted nonlocal coupled nonlinear Schrödinger equation are constructed by using the...     

Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects

Nonlinear Dynamics - In this paper, we study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum...     

Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics

In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.     

Excitation management of (2+1)-dimensional breathers for a coupled partially nonlocal nonlinear Schrödinger equation with variable coefficients

Nonlinear Dynamics - The Akhmediev-breather and Ma-breather solutions of a (2+1)-dimensional variable-coefficient coupled partially nonlocal nonlinear Schrödinger equation with non-localized...     

The bifurcation and exact travelling wave solutions of (1+2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity

By using the method of dynamical systems, this paper researches the bifurcation and the exact traveling wave solutions for a (1+2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Exact parametric representations of all wave solutions are given.     

Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity

Nonlinear Dynamics - In this work, we consider a nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity, which works as a model for the propagation of...