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Modulational Instability of Classical Water Waves
This is a brief exposition of the instability theory of Nguyen and Strauss (Comm. Pure Appl. Math., 2022). It is dedicated to the memory of Bob...
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Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions
A pair of one dimensional atomic chains which are coupled via the Klein-Gordon potential is considered in this study, with each chain experiencing...
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Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation
We consider the periodic standing waves in the derivative nonlinear Schrödinger (DNLS) equation arising in plasma physics. By using a newly developed...
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Modulational Instability of Surface-Gravity Waves in Presence of a Pycnocline of Finite Thickness
A nonlinear evolution equation is derived for surface gravity waves correct up to fourth order in wave steepness in the presence of a pycnocline of...
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Full description of Benjamin-Feir instability of stokes waves in deep water
Small-amplitude, traveling, space periodic solutions –called Stokes waves– of the 2 dimensional gravity water waves equations in deep water are...
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On the hyperbolic nonlinear Schrödinger equations
Here, we consider here Hyperbolic Nonlinear Schrödinger Equations (HNLS) that occur as asymptotic models in the modulational regime when the Hessian...
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Effect of Discrete Breathers on the Specific Heat of a Nonlinear Chain
A nonlinear chain with sixth-order polynomial on-site potential is used to analyze the evolution of the total-to-kinetic-energy ratio during...
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New Jacobi Elliptic Solutions and Other Solutions in Optical Metamaterials Having Higher-Order Dispersion and Its Stability Analysis
In this paper, we investigate the nonlinear Schrödinger equation in metamaterials having cubic-quintic nonlinearity with third and fourth order...
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Normal Form Transformations and Dysthe’s Equation for the Nonlinear Modulation of Deep-Water Gravity Waves
A new Hamiltonian version of Dysthe’s equation is derived for two-dimensional weakly modulated gravity waves on deep water. A key ingredient in this...
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Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence
A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence. The core physics in the...
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On the Momentary Stability of the Laminar Boundary Layer Beneath a Stokes Wave
The linear stability of the laminar boundary layer flow of a Stokes wave in deep waters is investigated by means of a ‘momentary’ criterion of...
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On the stability of solitary waves in the NLS system of the third-harmonic generation
We consider the NLS system of the third-harmonic generation, which was introduced in Sammut et al. (J Opt Soc Am B 15:1488–1496, 1998.). Our interest...
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Nonlinear Evolution Equations of Co-propagating Waves over Finite Depth Fluid
Using Zakharov integral equation approach, a pair of coupled non-linear evolution equations are derived for two co-propagating weakly nonlinear...
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Nonlinear gravity electro-capillary waves in two-fluid systems: solitary and periodic waves and their stability
Starting from the Euler equations governing the flow of two immiscible incompressible fluids in a horizontal channel, allowing gravity and surface...
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Mixed Higher-Order Rogue Waves and Solitons for the Coupled Modified Nonlinear Schrödinger Equation
The coupled modified nonlinear Schrödinger equation, which appears in birefringent optical fibers and describes the propagation of the short pluses...
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Numerical Simulations of Modulated Waves in a Higher-Order Dysthe Equation
The nonlinear stage of the modulational (Benjamin–Feir) instability of unidirectional deep-water surface gravity waves is simulated numerically by...
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Pattern formation in a 2-population homogenized neuronal network model
We study pattern formation in a 2-population homogenized neural field model of the Hopfield type in one spatial dimension with periodic...
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Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions
In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix...
