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Chirped periodic waves and solitary waves for a generalized derivative resonant nonlinear Schrödinger equation with cubic–quintic nonlinearity
We investigate the self-similar propagation of one-dimensional optical waves through optical fibers exhibiting self-steepening, dispersion,...
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Dynamics of localized waves for the higher-order nonlinear Schrödinger equation with self-steepening and cubic–quintic nonlinear terms in optical fibers
Under investigation in this paper is the dynamics of localized waves for the higher-order nonlinear Schrödinger equation with self-steepening and...
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The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods
The nonlinear Schrödinger hierarchy has a wide range of applications in modeling the propagation of light pulses in optical fibers. In this paper, we...
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Soliton-like nonlinear excitation in the FitzHugh–Nagumo cardiac model through the cubic–quintic complex Ginzburg–Landau equation
The article exclusively discusses how the cubic–quintic complex Ginzburg–Landau equation governs the dynamics of dissipative soliton in the...
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Novel solutions of the generalized mixed nonlinear Schrödinger equation with nonzero boundary condition
We present a determinant representation of generalized Darboux transformation for a generalized mixed nonlinear Schrödinger equation, and obtain...
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Localized solutions of inhomogeneous saturable nonlinear Schrödinger equation
In this paper, we obtain localized solutions of a nonhomogeneous saturable nonlinear system well described by a nonautonomous nonlinear Schrödinger...
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Whitham modulation theory and periodic solutions for the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain
In this paper, we investigate the periodic solutions and Whitham modulation theory for the fifth-order nonlinear Schrödinger equation, which can...
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Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation
In this work, we investigate rogue wave (RW) clusters of different shapes, composed of Kuznetsov–Ma solitons (KMSs) from the nonlinear Schrödinger...
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Dromion−like structures in a cubic−quintic nonlinear Schrödinger equation using analytical methods
We investigate the dromion-like excitations corresponding to intramolecular chain-like proteins. In the present work, the dromion-like excitations...
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Two-dimensional localized modes in saturable quintic nonlinear lattices
Stabilization of multidimensional solitons in self-focusing systems against the critical and supercritical collapse is a fundamental problem of...
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Peregrination, layers’ and multi-peaks’ generation induced by cubic-quintic-saturable nonlinearities and higher-order dispersive effects in a system of coupled nonlinear left-handed transmission lines
We establish a cubic-quintic-saturable nonlinear Schrödinger equation (CQSNLSE) with higher-order dispersive effects in a system of coupled nonlinear...
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Bright and kink solitons of time-modulated cubic–quintic–septic–nonic nonlinear Schrödinger equation under space-time rotated \(\mathcal{P}\mathcal{T}\)-symmetric potentials
This work focuses on the propagation behaviors and stabilities of solitons of a nonlinear Schrödinger equation with temporally inhomogeneous...
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High-speed excited multi-solitons in competitive power nonlinear Schrödinger equations
This paper deals with the competitive power nonlinear Schrödinger equation, which originates from the cubic-quintic model in physics. The equation...
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Multiple-peak and multiple-ring solitons in the nonlinear Schrödinger equation with inhomogeneous self-defocusing nonlinearity
We prove that inhomogeneous defocusing cubic (Kerr) nonlinear media described by the nonlinear Schrödinger equation, which could be realized in the...
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Equivalence transformations and differential invariants of a generalized cubic–quintic nonlinear Schrödinger equation with variable coefficients
In this paper, a variable-coefficient cubic–quintic nonlinear Schrödinger equation involving five arbitrary real functions of space and time is...
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Rogue waves on the double-periodic background for a nonlinear Schrödinger equation with higher-order effects
In this paper, we study the dynamics of rogue waves on the double-periodic background for a nonlinear Schrödinger equation with higher-order effects....
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Multi-elliptic rogue wave clusters of the nonlinear Schrödinger equation on different backgrounds
In this work, we analyze the multi-elliptic rogue wave clusters of the nonlinear Schrödinger equation (NLSE) in order to understand more thoroughly...
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Modulation instability and rogue waves for the sixth-order nonlinear Schrödinger equation with variable coefficients on a periodic background
In this paper, rogue wave solutions of a sixth-order focusing nonlinear Schrödinger (NLS) equation with variable coefficients are investigated on a...
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Coupled cubic-quintic nonlinear Schrödinger equation: novel bright–dark rogue waves and dynamics
In this paper, we investigate the coupled cubic-quintic nonlinear Schrödinger equation, which describes the effects of quintic nonlinearity on the...
