Results 81 to 90 of about 3,184 (198)

Novel Nonlinear Dynamical Solutions to the (2 + 1)‐Dimensional Variable Coefficients Equation Arise in Oceanography

Engineering Reports, Volume 7, Issue 6, June 2025.
This study explores novel nonlinear dynamical solutions to the (2 + 1)‐dimensional variable coefficient equation in oceanography. Using the Hirota bilinear method, we derive multi‐soliton, M‐lump, and hybrid wave solutions, revealing collision phenomena and their physical significance in nonlinear fluid dynamics and mathematical physics.
Hajar F. Ismael, Tukur Abdulkadir Sulaiman, Harivan R. Nabi, Shams Forruque Ahmed   +3 more
wiley   +1 more source

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.
This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
wiley   +1 more source

Retrieval of the optical soliton solutions of the perturbed Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity having the spatio‐temporal dispersion

Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2164-2178, 30 January 2025.
In this study, we obtained optical soliton solutions of the perturbed nonlinear Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity in the presence of spatio‐temporal dispersion. This equation models the propagation of optical pulses in fiber optic cables.
Ismail Onder, Aydin Secer, Muslum Ozisik, Mustafa Bayram   +3 more
wiley   +1 more source

Advanced Mathematical Approaches for the Kadomtsev–Petviashvili and Bogoyavlensky–Konopelchenko Equations in Applied Sciences

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
The Kadomtsev–Petviashvili (KP) equation and the Bogoyavlensky–Konopelchenko (BK) equation are fundamental models in the study of nonlinear wave dynamics, describing the evolution of weakly dispersive, quasi‐two‐dimensional (2D) wave phenomena in integrable systems.
Md. Abdul Aziz, Jingli Ren
wiley   +1 more source

On the Study of Nonlinear Murray Equation in Non‐Newtonian Fluids: Fractional Solitary Wave Structures, Chaos, and Sensitivity Demonstration

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This article introduces fractional solitary wave structures to the nonlinear Murray equation by applying advanced techniques, namely the generalized Arnous method and the modified generalized Riccati equation mapping method (MGREMM). This equation is known as a generalization of the nonlinear reaction–diffusion equation, which describes the diffusion ...
J. Muhammad, U. Younas, Haroon, H. Mukalazi, M. E. Meligy, K. A. Alnowibet, Shikha Binwal   +6 more
wiley   +1 more source

Abundant Families of Explicit Solitary Wave Structure for the Time‐Fractional Nonlinear Electrical Transmission Line Model With Its Modulation Instability

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this work, the abundant families of solitary wave solutions for the (2 + 1) dimensional time‐fractional nonlinear electrical transmission line (TFNLETL) model are investigated. To obtained these solutions, a well‐known approach is used namely, the Sardar subequation method.
Nadia Javed, Nauman Ahmed, Baboucarr Ceesay, Muhammad Zafarullah Baber, Kang-Jia Wang   +4 more
wiley   +1 more source

Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies.

, 1995
Hirota bilinear identity for Cauchy-Baker-Akhieser (CBA) kernel is introduced as a basic tool to construct integrable hierarchies containing lattice and q-difference times.
Bogdanov, Bogdanov, Grinevich, L.V. Bogdanov, Miwa, Segal, Zakharov, Zakharov   +7 more
core   +1 more source

Optical Soliton Structure Solutions, Sensitivity, and Modulation Stability Analysis in the Chiral Nonlinear Schrödinger Equation With Bohm Potential

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This study examines the optical soliton structure solutions, sensitivity, and modulation stability analysis of the chiral nonlinear Schrödinger equation (NLSE) with Bohm potential, a basic model in nonlinear optics and quantum mechanics. The equation represents wave group dynamics in numerous physical systems, involving quantum Hall and nonlinear ...
Ishrat Bibi, Shah Muhammad, Muhammad Shakeel, Baboucarr Ceesay, Ivan Giorgio   +4 more
wiley   +1 more source

Lump and Interaction solutions of a geophysical Korteweg–de Vries equation

Results in Physics, 2020
This manuscript retrieve lump soliton solution for geophysical Korteweg–de Vries equation (GKdVE) with the help of Hirota bilinear method (HBM). We will also obtain lump–kink soliton (which is interaction of lump with one kink soliton), lump-periodic ...
S.T.R. Rizvi, Aly R. Seadawy, F. Ashraf, M. Younis, H. Iqbal, Dumitru Baleanu   +5 more
doaj   +1 more source

Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
Various nonlinear evolution equations reveal the inner characteristics of numerous real‐life complex phenomena. Using the extended fractional Riccati expansion method, we investigate optical soliton solutions of the fractional Klein–Gordon equation within this modified framework.
Md. Abde Mannaf, Muktarebatul Jannah, Md. Habibul Bashar, Md. Ekramul Islam, Md. Zuel Rana, Mst. Tania Khatun, Md. Noor-A-Alam Siddiki, Md. Shahinur Islam, Shikha Binwal   +8 more
wiley   +1 more source