Modulation Instability in Magneto-electric Coupling Kerr-type Nonlinear Metamaterial

Quartic-dispersion-induced modulational instability in coupled nonlinear Chen–Lee–Liu systems

Intratumoral bacterial microbiota in gastrointestinal adenocarcinoma: From computational insights to clinical practice.

Understanding hydrogen diffusion is critical for improving the reliability and performance of oxide thin-film transistors (TFTs), where hydrogen plays a key role in carrier modulation and bias instability.

Propagation dynamics and modulation instability control in inhomogeneous nonlinear Schrödinger equation with two-photon absorption

Bilinearization, solitons and modulational instability for a variable-coefficient nonlocal Hirota equation

Investigating optical solitons and modulational instability in nonlinear metamaterials with quadratic-cubic nonlinearity

Study of the effect of modulation instability (MI) in transmission power, Brillouin gain and threshold power in stimulated Brillouin scattering (SBS) in long optical fibre

This paper presents the construction of exact wave solutions for the generalized nonlinear Schrödinger equation (NLSE) with second-order spatiotemporal dispersion using the modified exponential rational function method (mERFM). The NLSE plays a vital role in various fields such as quantum mechanics, oceanography, transmission lines, and optical fiber communications, particularly in modeling pulse dynamics extending beyond the traditional slowly varying envelope estimation. By incorporating higher-order dispersion and nonlinear effects, including cubic–quintic nonlinearities, this generalized model provides a more accurate representation of ultrashort pulse propagation in optical fibers and oceanic environments. A wide range of soliton solutions is obtained, including bright and dark solitons, as well as trigonometric, hyperbolic, rational, exponential, and singular forms. These solutions offer valuable insights into nonlinear wave dynamics and multi-soliton interactions relevant to shallow- and deep-water wave propagation. Conservation laws associated with the model are also derived, reinforcing the physical consistency of the system. The stability of the obtained solutions is investigated through the analysis of modulation instability (MI), confirming their robustness and physical relevance. Graphical representations based on specific parameter selections further illustrate the complex dynamics governed by the model. Overall, the study demonstrates the effectiveness of mERFM in solving higher-order nonlinear evolution equations and highlights its applicability across various domains of physics and engineering.

Addressing modulational instability in anti-resonant hollow-core fibers for pulse compression

Modulational instability and noise-driven dynamics in coupled nonlinear liquid crystal equations

Impact of fourth-order dispersion on modulation instability in a triple-core PIM-NIM-PIM-coupler with saturable function

The paper provides a dynamical study of the (2+1)-dimensional Zoomeron equation using the generalized Riccati equation mapping method. By applying an appropriate traveling wave transformation, the equation is reduced to an ordinary differential equation, enabling the construction of various solutions. There are several types of soliton solutions exhibited by the analysis including kink, anti-kink, bell structure or bright solitons, periodic soliton, anti-bell shape or dark soliton and W-shape soliton, singular periodic shape, singular bell shape and V-pattern solutions in terms of hyperbolic and trigonometric functions. The solutions prove rich in understanding the nonlinear wave phenomena of the Zoomeron model. Nonlinear dynamics are investigated using bifurcation, chaotic, sensitivity and stability analysis that uncover complex solution behaviors and stability regimes. This work first and exclusively presents new V-pattern and W-shaped soliton solutions of the (2+1)-dimensional Zoomeron equation by using considered method and offers the first systematic study of their transition from periodic to chaotic behavior. Modulation instability analysis verifies the stability of soliton structures against perturbations. To demonstrate the features and evolution of the solutions, detailed graphical representations are presented, such as 3D surface plots, 2D profiles and contour plots. These visualizations demonstrate the dynamic behaviors and structural properties of the resultant soliton solutions, exemplifying the efficiency of the generalized Riccati equation mapping method for studying intricate nonlinear systems.

Signature of second stable regime of modulational instability and rogue wave triplets in dual-polarity dusty plasmas

This study investigates the wave structures and qualitative assessment of a two-dimensional vector nonlinear Schrödinger equation (2D VNLSE) that occurs in Bose–Einstein condensates (BECs) and nonlinear optics. We convert the vector PDE form into two linked scalar PDEs to yield optical vortex structures of the governing model. We create different optical soliton solutions using the Kudryashov and the sine-Gordon expansion methods. We present their 3D, 2D, and density maps to allow for a comprehensive and understandable representation of their underlying physical patterns. Furthermore, we assess the system’s qualitative behavior by analyzing its obvious characteristics, such as modulation instability, sensitivity, bifurcation, and chaos detection, and we give accompanying illustrations to support our conclusions. This study’s accomplishment allows researchers to examine the dynamics and growth of optical solitons and vortices in nonlinear systems in greater detail, which opens up important possibilities with broad significance in many scientific and technological fields.

Novel geometric insights into modulation instability and soliton solutions of the truncated M-fractional $(3+1)$-D generalized Painlevé equation

The modulational instability, classifications and dynamical properties of the localized wave solutions in the Hirota equation

Modulation instability, stochastic soliton dynamics, and analytical solutions in the Fokas-Lenells equation with quadratic-cubic nonlinearity

A unified analytical framework for chaos, sensitivity, and modulation instability with exact solutions of a newer form of Boussinesq equation

Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model