Results 71 to 80 of about 11,580,339 (146)

Nonlinear Dynamics of the Nonlinear Schrödinger Equation via an Improved Modified Extended Tanh‐Function Algorithm

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This work investigated optical soliton solutions to the perturbed Schrödinger–Hirota equation with a generalized cubic–quintic–septic nonlinearity law involving spatiotemporal dispersion. Our study employs an improved modified extended tanh‐function method to obtain a comprehensive set of 18 soliton solutions, including bright, dark, singular, periodic,
Saja Faeq Noaman, Huda Jawad, Noor A. Abdulhmeed, Saja Saeed Abed, Shikha Binwal   +4 more
wiley   +1 more source

Novel optical structures for the cubic-quartic nonlinear Schrödinger equation: Analytical and numerical perspectives

Ain Shams Engineering Journal
The current paper uses both analytical and numerical approaches to explore the cubic-quartic nonlinear Schrödinger model governed by the Kerr law. For the analytical analysis, we employ the addendum to Kudryashov's method that yields several intriguing ...
Afrah M. Almalki, A.A. Alshaery, H.O. Bakodah   +2 more
doaj   +1 more source

Exploring Advanced Soliton Solutions for the Stochastic Nonlinear System With Temporal Fractionality: Multiplicative Noise Intensity, Modulation Instability, and Chaotic Nature

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study investigates the stochastic fractional new coupled Konno–Oono equation with external forced multiplicative noise, focusing on the chaotic nature, the influence of multiplicative noise intensity, and the fractionality parameter on exact soliton solutions. The proposed model is used to describe the complex phenomena in the magnetic field.
Md. Mamunur Roshid, Ramy M. Hafez, Mahtab Uddin, Yakup Yildirim, Golam Mostafa, Zuo Da-Wei   +5 more
wiley   +1 more source

Travelling wave solutions and conservation laws of the (2+1)-dimensional new generalized Korteweg–de Vries equation

Partial Differential Equations in Applied Mathematics
In this study, we investigate the travelling wave solutions of the (2+1)-dimensional new generalized Korteweg–de Vries equation by employing Lie group analysis along with various techniques which include direct integration, simplest equation method and ...
Boikanyo Pretty Sebogodi, Chaudry Masood Khalique   +1 more
doaj   +1 more source

Dynamics of Computational Solitons: Modulation Instability, Bifurcation, Chaotic Nature With Different Chaos‐Detecting Tools, and Influence of Multiplicative Noise Intensity

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study presents the dynamic analysis of stochastic fractional unstable nonlinear Schrödinger equation (SFuNLSE), focusing on the analysis of bifurcation, chaotic nature, return map, recurrence plots, strange attractor, basin attractor, power spectrum, chaotic nature and also finds the exact optical soliton solution with multiplicative noise ...
Md. Mamunur Roshid, Mohamed Abdalla, M. S. Osman, Smritijit Sen   +3 more
wiley   +1 more source

Abundant dynamical structure of solutions to truncated M-fractional modified Korteweg–de Vries model: Effects of dispersion, nonlinearity and fractionality

, 2023
This work explores various wave pattern dynamics due to fractional derivative, dispersive and nonlinearity effects for the nonlinear time M-fractional modified Korteweg–de Vries (tM-fMKDV) model.
M. Zulfikar Ali, M.F. Hoque, Hadi rezazadeh, Mst. Shekha Khatun   +3 more
core   +1 more source

An extended Korteweg-de Vries equation: Multi-soliton solutions and conservation laws

, 2017
In this paper, we consider an extended KdV equation, which arises in the analysis of several problems in soliton theory. First, we converted the underlying equation into the Hirota bilinear form. Then, using the novel test function method, abundant multi-

core   +1 more source

On obtaining optical solitons of the perturbed cubic-quartic model having the Kudryashov’s law of refractive index

This article delves into the study of the perturbed cubic-quartic Kudryashov’s equation having the Kudryashov’s law of refractive index which is recently introduced to the literature.
BAYRAM, Mustafa, ÖZIŞIK, Müslüm, ÇINAR, Melih, SEÇER, Aydın, Cakicioglu, Hasan   +4 more
core   +1 more source

Unveiling the Dynamics of Nonlinear Landau-Ginzburg-Higgs (LGH) Equation: Wave Structures through Multiple Auxiliary Equation Methods

Journal of New Theory
This comprehensive investigation delves deeply into the intricate dynamics governed by the nonlinear Landau-Ginzburg-Higgs equation. It uncovers a diversity of semi-analytical solutions by leveraging three auxiliary equation methods within the traveling ...
Şerife Müge Ege
doaj   +1 more source

Abundant solitons for highly dispersive nonlinear Schrödinger equation with sextic-power law refractive index using modified extended direct algebraic method

Alexandria Engineering Journal
In this paper, we investigate soliton solutions and other exact solutions of the highly dispersive perturbed nonlinear Schrödinger equation having Kudryashov's arbitrary form with sextic-power law of refractive index and generalized non-local laws ...
Wafaa B. Rabie, Hisham H. Hussein, Hamdy M. Ahmed, Mahmoud Alnahhass, Wassim Alexan   +4 more
doaj   +1 more source