Results 81 to 90 of about 3,238 (183)

Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

Complexity, 2019
In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton
Baoyong Guo, Huanhe Dong, Yong Fang
doaj   +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

Painleve equations from Darboux chains - Part 1: P3-P5

, 2003
We show that the Painleve equations P3-P5 can be derived (in a unified way) from a periodic sequence of Darboux transformations for a Schrodinger problem with quadratic eigenvalue dependency.
Bureau F J, Clarkson P A, Degasperis A, Fordy A P, Hietarinta J, Hietarinta J, Hietarinta J Willox R, Jarmo Hietarinta, Jimbo M, Malmquist J, Matveev V B, Noumi M, Noumi M, Noumi M, Noumi M, Ohta Y, Okamoto K, Okamoto K, Okamoto K, Okamoto K, Okamoto K, Okamoto K, Okamoto K, Ralph Willox, Sato M, Schief W K, Shabat A, Shabat A, Shabat A, Shabat A, Takasaki K, Veselov A P, Willox R   +32 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

Construction of Nth-order rogue wave solutions for Hirota equation by means of bilinear method [PDF]

, 2014
In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants.
Mu, Gui, Qin, Zhenyun
core  

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

Unification of integrable q-difference equations

Electronic Journal of Differential Equations, 2015
This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions ...
Burcu Silindir, Duygu Soyoglu
doaj  

Novel Soliton and Wave Solutions for the Dual‐Perturbed Integrable Boussinesq Equation

Complexity, Volume 2025, Issue 1, 2025.
Nonlinear science represents a foundational frontier in scientific inquiry that explores the shared characteristics inherent in nonlinear phenomena. This study focused on the perturbed Boussinesq (PB) equation incorporating dual perturbation terms. Soliton solutions were deduced by leveraging the traveling wave hypothesis. Furthermore, by employing the
Akhtar Hussain, Tarek F. Ibrahim, Faizah D. Alanazi, Waleed M. Osman, Arafa A. Dawood, Jorge Herrera, Xianggui Guo   +6 more
wiley   +1 more source

A Study of the Wave Dynamics for the Reaction‐Diffusion Brusselator System and RKL Equation

Discrete Dynamics in Nature and Society, Volume 2025, Issue 1, 2025.
In this article, the reaction‐diffusion Brusselator system and the Radhakrishnan, Kundu, and Laskshmanan (RKL) equation are discussed. The investigation is focused on the solution procedure of the nonlinear evolution equations in chemical and biological processes.
Onur Alp İlhan, Jalil Manafian, Deepali
wiley   +1 more source

Discretisations of constrained KP hierarchies [PDF]

, 2014
We present a discrete analogue of the so-called symmetry reduced or `constrained' KP hierarchy. As a result we obtain integrable discretisations, in both space and time, of some well-known continuous integrable systems such as the nonlinear Schroedinger ...
Hattori, Madoka, Willox, Ralph
core   +2 more sources