Related Experiment Video
Updated: Sep 8, 2025

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
Some novel optical pulses in hydrodynamical nonlinear complex equation using M-truncated fractional derivative
Esin Ilhan1, Shafqat Ur Rehman2, Muhammad Bilal3
1Faculty of Engineering and Architecture, Kirsehir Ahi Evran University, Kirsehir, Turkey.
Abstract:
This study investigates soliton solutions and dynamic wave structures in the complex Ginzburg-Landau (CGL) equation, which is crucial for understanding wave propagation in various physical systems. We employ three analytical methods: the Kumar-Malik method, the generalized Arnous method, and the energy balance method to derive novel closed-form solutions. These solutions exhibit diverse solitonic phenomena, including multi-wave solitons, complex solitons, singular solitons, periodic oscillating waves, dark-wave, and bright-wave profiles. Our results reveal new families of exact solitary waves via the generalized Arnous method and diverse soliton solutions through the Kumar-Malik method, including hyperbolic, trigonometric, and Jacobi elliptic functions. Verification is ensured through back-substitution to the considered model using Mathematica software. Additionally, we plot the various graphs with the appropriate parametric values under the influence of the M-truncated fractional derivative to visualize the solution behaviors with varying parameter values. This research contributes significantly to understanding wave dynamics in physical oceanography, and the unique outcomes explored in this research will play a vital role for the forthcoming investigation of nonlinear equations.
More Related Videos
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Convergence of Fourier Series
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Damped Oscillations
Although friction and other non-conservative...
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
Second Order systems II

