Work

Nonlinear Stochastic Wave Behavior: Soliton Solutions and Energy Analysis of Kairat-II and Kairat-X Systems

Year: 2025

Type: article

Abstract: We study stochastic variants of the Kairat-II and Kairat-X equations in (3 + 1) dimensions, two canonical models in soliton theory. Random fluctuations are incorporated through a Wiener process, yielding a multiplicative stochastic embedding of the wave fields. By combining the enhanced direct algebraic technique with the new projective Riccati equation approach, we obtain closed-form stochastic soliton solutions and analyze how noise modulates their amplitude and localization. The solutions are illustrated with consistent 3D surface plots (mean field vs. sample paths) and 2D time traces to highlight wave geometry and variability. In addition, we employ the energy balance approach to separate kinetic and potential contributions and to verify an energy balance relation for the derived solutions, thereby clarifying their physical plausibility and stability under noise. The results provide exact, easily verifiable benchmarks for stochastic nonlinear wave models and a practical template for incorporating randomness into nonlinear dispersive systems.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9110728

Authors: Syed T. R. Rizvi, Lotfi Jlali, Iqra Anjum, Husnain Abad, Emad Solouma, Aly R. Seadawy

Institutions: COMSATS University Islamabad, Imam Mohammad ibn Saud Islamic University, Taibah University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Al-Imam Muhammad Ibn Saud Islamic University