Exploring the impact of Brownian motion on novel closed-form solutions of the extended Kairat-II equation

PLoS ONE, Journal Year: 2025, Volume and Issue: 20(1), P. e0314849 - e0314849

Published: Jan. 16, 2025

This work considers a stochastic form of an extended version the Kairat-II equation by adding Browning motion into deterministic equation. Two analytical approaches are utilized to derive solutions modified The first method is Tanh technique linked with Riccati equation, which implemented extract some closed-form in tangent and cotangent functions. second Sardar sub-equation (SSEM) used attain several trigonometric hyperbolic Solutions selected randomly from large families suggested techniques visualized 3D 2D scenarios. From simulations intriguing observation made: generated through tanh exhibit singular nature, hybrid waves among them. On contrary this, derived SSEM, tend be mostly non-singular nature. varying influence noise intensity revealed that high amplitude energy regions more vulnerable induced as compared lower regions, relatively robust. study introduces novel incorporating Brownian providing new insights behavior integrable systems have not been previously explored.

Language: Английский

Qualitative analysis and new traveling wave solutions for the stochastic Biswas-Milovic equation

AIMS Mathematics, Journal Year: 2025, Volume and Issue: 10(2), P. 4092 - 4119

Published: Jan. 1, 2025

Language: Английский

Investigating the Dynamics of a Unidirectional Wave Model: Soliton Solutions, Bifurcation, and Chaos Analysis

Fractal and Fractional, Journal Year: 2024, Volume and Issue: 8(11), P. 672 - 672

Published: Nov. 18, 2024

The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems phenomena. This investigation has two primary aims. First, it employs novel modified Sardar sub-equation method, not yet explored the literature, derive new solutions for governing model. Second, analyzes dynamical structure of model using bifurcation, chaos, sensitivity analyses. To provide more accurate depiction underlying dynamics, they use quantum mechanics explain intricate behavior system. illustrate physical obtained solutions, 2D 3D plots, along with phase plane analysis, are presented appropriate parameter values. These results validate effectiveness employed providing thorough consistent significant computational efficiency. investigated soliton will be valuable understanding structures various scientific fields, including ferromagnetic nonlinear optics, theory, fiber optics. approach proves highly effective handling complexities inherent mathematical problems, especially those involving fractional-order systems.

Language: Английский