Results 31 to 40 of about 155 (137)

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Diverse Soliton Structures of Induced Curves in the Integrable Coupled Kuralay Equation

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This study explores the integrable coupled Kuralay equation, which is widely utilized to study the motion of induced curves. In fields such as ferromagnetic materials, nonlinear optics, and optical fibers, soliton solutions of the Kuralay equation have emerged as significant recent developments.
Shah Muhammad, Muhammad Shakeel, Muhammad Abuzar, Tereda Seifu Neda, Ivan Giorgio   +4 more
wiley   +1 more source

Multiple soliton and M-lump waves to a generalized B-type Kadomtsev–Petviashvili equation

Results in Physics, 2023
In this study, we focus on the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which is useful for modeling weakly dispersive waves transmitted in quasi media and fluid mechanics.
Hajar F. Ismael, Harivan R. Nabi, Tukur Abdulkadir Sulaiman, Nehad Ali Shah, Mohamed R. Ali   +4 more
doaj   +1 more source

Dynamical Behavior and Chaotic Nature of M‐Fractional Paraxial Wave Equation With Three Analytical Methods

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid, Mahtab Uddin, Mohammad Safi Ullah, Golam Mostafa, Ashek Ahmed, Shikha Binwal   +5 more
wiley   +1 more source

Constructing Traveling Wave Solutions via a Generalized Expansion Method for Nonlinear Evolution Equations Possessing Variable Coefficients

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor, Xianhua Song, Muhammad Shakeel, Muhammad Qamar Fareed, Baboucarr Ceesay, Kang-Jia Wang   +5 more
wiley   +1 more source

New interaction solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation

Results in Physics, 2022
This study aims to determine novel analytical lump solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation through conducting symbolic computations using the Hirota direct method.
Fei Long, Shami A.M. Alsallami, S. Rezaei, Kamsing Nonlaopon, E.M. Khalil   +4 more
doaj   +1 more source

The Two Modified G′G‐Expansion Methods for Obtaining Solitons of the Korteweg‐De Vries Equation

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
The Korteweg‐de Vries (KdV) equation plays an important role in describing the propagation of water waves in shallow channels. Several analytical methods, such as tanh‐function methods (TFMs), exponential function method, and Jacobi elliptic function method, provide the exact solitons to the KdV equation.
Emmanuel Mensah, Benedict Barnes, Isaac Kwame Dontwi, Kwaku Forkuoh Darkwah, Onur Alp Ilhan   +4 more
wiley   +1 more source

Multistructure Novel Stochastic Soliton Solutions for the (2+1)‐Dimensional Breaking Wave Equation Within the Fractional Derivative Influence

Complexity, Volume 2026, Issue 1, 2026.
In this paper, we investigate the exact stochastic solutions of the (2 + 1)‐dimensional stochastic fractional‐space breaking soliton equation (SFSBSE) involving the truncated M‐fractional derivative in space. This equation models a range of physical phenomena, including fluid wave propagation, shallow water dynamics, and plasma physics, under the ...
Fatma Nur Kaya Sağlam, Volkan Ala, Bahadır Kopçasız, Ercan Çelik, Lingzhong Guo   +4 more
wiley   +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

Lump-soliton interaction solutions to differential-difference mKdV systems in (2+1)-dimensions

Results in Physics
Lump-soliton interaction solutions to continuous integrable systems have been pretty well studied, but there are relatively few results in the differential-difference (DΔ) case.
Kai Zhou, Ya-Nan Hu, Jun-Da Peng, Kai-Zhong Shi, Shou-Feng Shen, Wen-Xiu Ma   +5 more
doaj   +1 more source