Results 61 to 70 of about 132,714,206 (184)

Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

Journal of Ocean Engineering and Science, 2023
By taking advantage of three different computational analytical methods: the Lie symmetry analysis, the generalized Riccati equation mapping approach, and the modified Kudryashov approach, we construct multiple new analytical soliton solutions to the ...
Shoukry El-Ganaini, Sachin Kumar, Monika Niwas   +2 more
doaj   +1 more source

Kudryashov Expansion Method Applied to Fisher Mathematical Model

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
We obtain new computational soliton solutions characterized by topological, rational, exponential, trigonometric, and hyperbolic functions for the Fisher equation. Using a good strategy, the Kudryashov expansion method is used to find different dynamical wave structures of soliton solutions within the scope of evolutionary dynamical structures of ...
Elif Deniz Öztürk, Ercan Çelik, Sıdıka Şule Şener Kiliç, Kang-Jia Wang   +3 more
wiley   +1 more source

Optical soliton solutions of Schrödinger–Hirota equation with parabolic law nonlinearity via generalized Kudryashov algorithm [PDF]

, 2023
The aim of this study is to peruse the dispersive Schrödinger–Hirota equation (SH equation) with parabolic law linearity to get optical soliton solutions by utilizing the generalized Kudryashov method (GKM).
Bayram, Mustafa, Çakıcıoğlu, Hasan, Seçer, Aydın, ÖZIŞIK, Müslüm, Özışık, Müslüm, Cakicioglu, Hasan, Hasan Cakicioglu, Aydin Secer, Mustafa Bayram, Muslum Ozisik   +9 more
core   +1 more source

Optical Soliton Solutions and Modulation Instability of the Higher‐Order Complex Cubic‐Quintic Ginzburg–Landau Equation

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
The propagation of ultrashort optical pulses in nonlinear dissipative media is investigated through a generalized higher‐order cubic–quintic complex Ginzburg–Landau equation (HG CQ‐CGLE) incorporating third‐order dispersion (TOD), fourth‐order dispersion (FOD), self‐steepening (SS), and intrapulse Raman scattering (IRS) effects.
Alfred Dang A Mekoung, Nicodème Djiedeu, Jean Pierre Nguenang, Antonio Scarfone   +3 more
wiley   +1 more source

Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods

Mathematics
This paper presents an investigation into original analytical solutions of the (2+1)-dimensional combined potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations.
Muath Awadalla, Arzu Akbulut, Jihan Alahmadi   +2 more
doaj   +1 more source

Numerical Simulations of Coupled Solitary Waves With Spatially Modulated Non‐Linearity

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This study investigates the dynamics of two coupled solitary waves propagating in media characterised by spatially modulated non‐linearity and variable dispersion. By employing numerical simulations of a system of coupled non‐linear Schrödinger equations (NLSEs) with varying coefficients, we analyse how inhomogeneous physical properties influence ...
Ngaka John Nchejane, Mabatho Thakedi, Shikha Binwal   +2 more
wiley   +1 more source

New Results of Some of the Conformable Models Arising in Dynamical Systems

Advances in Mathematical Physics, 2022
This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method.
Md Nur Alam, Onur Alp Ilhan, Jalil Manafian, Muhammad Imran Asjad, Hadi Rezazadeh, Haci Mehmet Baskonus   +5 more
doaj   +1 more source

Dynamical Optical Structure Solutions of the Time‐Fractional Chen‐Lee‐Liu Equation

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
In this article, we utilize the conformable fractional (CF) derivative to investigate the analytically innovative soliton solutions for the time‐fractional nonlinear perturbed Chen‐Lee‐Liu (CLL) equation in optical fibers. An essential governing equation in nonlinear optics, the perturbed CLL model describes the propagation of ultrashort pulses in ...
Shah Muhammad, Abdul Saboor, Muhammad Shakeel, Hameed Gul Ahmadzai, Ivan Giorgio   +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

Optical solitons of the Kudryashov Equation via an analytical technique [PDF]

, 2022
Some new optical solitons find for the Kudryashov equation (KE) in this study. These solutions are in the form of dark, bright, singular, singular-dark solitons and other solutions with certain conditions.
Bayram, Mustafa, Tala Tebue, Eric, Raheel, Muhammad, İnç, Mustafa, Mustafa Inc, E. Tala-Tebue, M. Raheel, Mustafa Bayram   +7 more
core   +1 more source