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Travelling-wave, Mixed-lump-kink and Mixed-rogue-wave-kink Solutions for an Extended (3+1)-dimensional Shallow Water Wave Equation in Oceanography and Atmospheric Science
Shallow water waves are seen in oceanography, atmospheric science, and other fields. In this paper, we investigate an extended (3+1)-dimensional...
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Modulation instability—rogue wave correspondence hidden in integrable systems
The bulk-boundary correspondence is a key feature of topological physics and is universally applicable to Hermitian and non-Hermitian systems. Here,...
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Resonant multiple soliton and rogue type multiple lump wave solutions of the modified KdV–KP equation
This study investigates the precise solutions of the (2+1)-dimensional modified KdV–KP equation. Resonant multiple soliton solutions are examined by...
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Comparative Study of Rogue Wave Solutions for Autonomous and Non-autonomous Saturable Discrete Nonlinear Schrödinger Equation
The existence of rogue waves in the saturable discrete nonlinear Schrodinger equation (SDNLSE) has been established numerically. These extreme waves...
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Exploring the Salerno Model for Rogue Wave Generation: A Linear Stability Analysis Beyond the DNLS and AL Limits
This study presents a detailed analysis of the Salerno equation, which is a novel mathematical model for rogue wave generation. The model bridges the...
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Akhmediev and Kuznetsov–Ma rogue wave clusters of the higher-order nonlinear Schrödinger equation
In this work, we analyze three types of rogue wave (RW) clusters for the quintic nonlinear Schrödinger equation (QNLSE) on a flat background. These...
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Breathers-like rogue wave trains induced by nonlinear dynamics of DNA breathing
We introduce in the deoxyribonucleic acid (DNA) molecular chain at the first time the collective coordinates’ theory to measure the exact signature...
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The generalized Darboux transformation and higher-order rogue waves for a coupled nonlinear Schrödinger system with the four-wave mixing terms in a birefringent fiber
Optical communication systems play a role in the modern long-distance communication networks due to their characteristics of the low-loss...
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Hybrid rogue wave and breather solutions for a complex mKdV equation in few-cycle ultra-short pulse optics
We report exotic hybrid rogue wave and breather solutions for a complex mKdV equation describing soliton dynamics in few-cycle ultra-short pulse...
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Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions
The current study deals with investigation of Einstein’s vacuum field equation (EVFE) for exploring various lumps, breathers and interaction...
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Multiple solitons solutions, lump solutions and rogue wave solutions of the complex cubic Ginzburg–Landau equation with the Hirota bilinear method
In this paper, we obtain the exact solutions of the (1+1) dimensional complex cubic Ginzburg–Landau equation (CCGLE) by using the Hirota bilinear...
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Dynamics of Rogue waves in one-dimensional acoustic transmission line metamaterials
Analytically, modulational instability phenomenon and Rogue wave propagation are studied in an acoustic metamaterial based on the one-dimensional...
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Real-time observation of optical rogue waves in spatiotemporally mode-locked fiber lasers
Fiber lasers offer tabletop nonlinear environments to mimic and study the complex dynamics of nature. Optical rogue waves, rarely occurring extreme...
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Breather, kink and rogue wave solutions of Sharma-Tasso-Olver-like equation
In this paper, we consider the Sharma-Tasso-Olver-Like equation (STOLE) describing the dynamical behaviour of nonlinear dispersive waves in...
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Coupled Hirota system: higher-order rogue waves and multi-solitons structures
In this work, the higher-order localized waves for a coupled Hirota system are analytically investigated, providing a way to describe the wave...
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Modulation instability spectrum and rogue waves of the repulsive lattices
In this work, the modulation instability and solitonic rogue waves are addressed in the repulsive lattice formed by identical particles with nearest...
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Exotic rogue waves in an extended nonlocal nonlinear Schrödinger equation with self-induced PT-symmetric potentials
We consider the spectral problem and adjoint problem for an extended nonlocal nonlinear Schrödinger (NLS) equation. Utilizing the Schur polynomial...
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Rogue wave patterns to the artificial synchronization of three uncoupled Ablowitz−Ladik systems in the framework of Babalic−Cârstea auxiliary Lax representation
The artificial synchronization of three uncoupled Ablowitz−Ladik systems associated with the sixth-order auxiliary linear problem is investigated...
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Deformation of inhomogeneous vector optical rogue waves in the variable coefficients coupled cubic–quintic nonlinear Schrödinger equations with self-steepening
In this study, we explore variable coefficients coupled cubic–quintic nonlinear Schrödinger (CQNLS) equations with self-steepening, modeling optical...
