Article
Mathematics, Interdisciplinary Applications
S. A. El-Tantawy, Alvaro H. Salas, M. R. Alharthi
Summary: In this work, novel analytic traveling wave solutions including the cnoidal and solitary wave solutions of the planar Extended Kawahara equation are deduced using four different analytical methods. These solutions may be useful for researchers interested in studying nonlinear wave propagation in various branches of science.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
Rania A. Alharbey, Wasayf R. Alrefae, Hunida Malaikah, Elsayed Tag-Eldin, Samir A. El-Tantawy
Summary: In this investigation, the nonplanar modified fifth-order Korteweg-de Vries equation (nmKdV5), also known as the nonplanar modified Kawahara equation (nmKE), is solved using the ansatz approach. Two general formulas for the semi-analytical symmetric approximations are derived, and the obtained solutions are applied to the fluid equations for electronegative plasmas. The obtained approximations can be used by researchers interested in studying nonlinear phenomena in plasma physics to interpret their experimental and observational findings.
Article
Multidisciplinary Sciences
Sadah A. Alkhateeb, S. Hussain, Wedad Albalawi, S. A. El-Tantawy, E. I. El-Awady
Summary: The effects of Landau quantization magnetic field, the Coriolis force, and collisional frequency on the properties of dissipative ion acoustic waves (IAWs) are discussed using the two-dimensional fluid quantum hydrodynamic (QHD) as the basis. The damped Korteweg-de Vries (KdV) equation, derived using the reductive perturbation technique (RPT), fails to accurately describe the system as observed in laboratory experiments. A new non-integrable differential equation, the damped Kawahara equation, is introduced to account for higher-order effects. A semi-analytical solution is derived to understand the features of quantum IAWs in astrophysical plasmas and novel materials like graphene and topological insulators.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
(2023)
Article
Mechanics
S. A. El-Tantawy, L. S. El-Sherif, A. M. Bakry, Weaam Alhejaili, Abdul-Majid Wazwaz
Summary: In this work, the non-integrable nonplanar damped Kawahara equation is solved and analyzed analytically. Two general formulas for analytical approximations are derived, which can be applied to study nonlinear and complicated phenomena in various fields.
Article
Physics, Multidisciplinary
Muhammad Khalid, Hayat Khan, Lal Said Jan, Badriah M. Alotaibi
Summary: This paper investigates the existence and properties of dissipative solitons in a superthermal plasma with pressure anisotropy. It is found that anisotropic pressure can influence the formation, lifetime and spatial structure of the solitons. This research is of importance for space and astrophysical plasma systems, laboratory plasmas, and fusion research.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
S. A. El-Tantawy, Alvaro H. Salas, Haifa A. Alyousef, M. R. Alharthi
Summary: In this study, a set of novel exact and approximate solutions to the forced damped Kawahara equation are derived. The ansatz method and other techniques are employed to obtain the solutions. This investigation is of great importance for studying nonlinear phenomena in various scientific fields.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Engineering, Marine
Noufe H. Aljahdaly, S. A. El-Tantawy
Summary: A novel approximate analytical solution to the linear damped Kawahara equation is presented, which can be used to study the properties of dissipative traveling waves and solve various non-integrable evolution equations related to realistic natural phenomena.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Multidisciplinary Sciences
Gang Xu, Alexander U. Nielsen, Bruno Garbin, Lewis Hill, Gian-Luca Oppo, Julien Fatome, Stuart G. Murdoch, Stephane Coen, Miro Erkintalo
Summary: Researchers observed spontaneous symmetry breaking of dissipative optical solitons in a nonlinear optical ring resonator, leading to the coexistence of distinct vectorial solitons with asymmetric polarization states. By perturbing the system, deterministic switching between the two symmetry-broken dissipative soliton states can be achieved. This work provides fundamental insights into multi-mode nonlinear optical resonators, dissipative structures, and spontaneous symmetry breaking in coherently driven Kerr resonators.
NATURE COMMUNICATIONS
(2021)
Article
Mechanics
Haifa A. Alyousef, Alvaro H. Salas, R. T. Matoog, S. A. El-Tantawy
Summary: This study presents a detailed investigation on the completely non-integrable forced damped Gardner/Extended Kawahara equation (FDEKE) and proposes three techniques to approximate the equation. The properties of periodic forced dissipative extended Kawahara solitary and cnoidal waves are analyzed numerically and analytically, and the accuracy of the obtained approximations is evaluated. The study highlights the potential applications of these approximations in various fields.
Article
Multidisciplinary Sciences
Sherif M. E. Ismaeel, Abdul-Majid Wazwaz, Elsayed Tag-Eldin, Samir A. El-Tantawy
Summary: This work analyzes a damped modified Kawahara equation with cubic nonlinearity and two dispersion terms. An effective semi-analytical method is employed to find approximate solutions to the equation. The derived formulas can be used to study various types of traveling waves described by the equation. The results contribute to explaining nonlinear phenomena in different fields such as plasma physics and nonlinear optics.
Article
Engineering, Electrical & Electronic
Zara Kasapeteva, Aneliya Dakova, Stefka Krasteva, Valeri Slavchev, Diana Dakova, Lubomir Kovachev, Anjan Biswas
Summary: This study analytically investigates the propagation of bright solitons in single-mode fibers under the influence of third-order linear dispersion and self-steepening effect. New analytical solutions in the form of cnoidal waves are found, which can be reduced to sech-solitons under certain parameter values.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Physics, Fluids & Plasmas
Ning Mao, Li-Chen Zhao
Summary: Exact analytical soliton solutions are essential in the field of solitons. We have successfully obtained analytical vector soliton solutions and removed conventional constraints in coupled systems. These results are important in observing novel vector solitons in experimental settings.
Article
Astronomy & Astrophysics
B. Snow, A. Hillier
Summary: This study investigates the impact of collisional ionisation and recombination in slow-mode partially ionised shocks. It is found that considering ionisation, recombination, and ionisation potential significantly alters the behavior of shocks, especially in substructure and post-shock regions. Multi-fluid effects can lead to substantial deviations from magnetohydrodynamic results in various partially ionised plasmas, such as the solar chromosphere and molecular clouds.
ASTRONOMY & ASTROPHYSICS
(2021)
Article
Mathematics, Applied
Patrick Sprenger, Thomas J. Bridges, Michael Shearer
Summary: The Kawahara equation is a weakly nonlinear longwave model that describes dispersive waves. It is derived by balancing the third-order dispersive effects with a fifth-order correction. The equation has a Hamiltonian structure and admits a two-parameter family of single-phase periodic solutions. Jump conditions are derived for pairs of periodic solutions with equal speed and Hamiltonian, which are necessary for the existence of traveling waves. Bifurcation theory and parameter continuation are used to construct multiple solution branches.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Computer Science, Interdisciplinary Applications
Aiman Zara, Fayyaz Ahmad, Salima Kouser, Anjum Pervaiz, Shafiq Ur Rehman
Summary: In this article, a numerical approximation of the modified Kawahara equation is investigated using the Kernel smoothing method. The spatial derivatives are approximated using the smoothing Kernel method, while the time integration is performed using the Crank-Nicolson method. The conservative nature of the proposed scheme is demonstrated using the mass conservation constant and energy conservation constant, and numerical testing on a collection of test problems is conducted to evaluate the quality of the proposed scheme.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Engineering, Multidisciplinary
Alvaro H. Salas, S. A. El-Tantawy, Noufe H. Aljahdaly
Summary: The study focused on nonlinear equations of motion rarely addressed in classical dynamics education, deriving new analytical solutions and comparing them with numerical solutions.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
S. A. El-Tantawy, Alvaro H. Salas, M. R. Alharthi
Summary: This study presents a novel analytical solution and an approximate analytical solution to the Duffing equation with constant forced term, with comparisons to the Runge-Kutta fourth-order method. The solutions simplify complex oscillator equations and are applied to investigate signal oscillations in RLC circuits.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Alvaro H. Salas, Castillo H. Jairo E, M. R. Alharthi
Summary: This paper presents novel solutions to the family of Helmholtz equations, including some reported equations. The analytical solutions for equation (1) were obtained using direct and indirect techniques, while equation (2) was solved with a new ansatz and the help of equation (1) solutions. The numerical solutions for the evolution equations were calculated using the Adomian decomposition method, and a comparison between approximate analytical and numerical solutions was performed. Additionally, the characteristics of (un)damping oscillations in a degenerate quantum plasma model were investigated as a practical application.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Mechanics
S. A. El-Tantawy, Alvaro H. Salas, M. R. Alharthi
Summary: In this study, dissipative cylindrical and spherical electrostatic low-frequency dust-acoustic waves in a strongly coupled dusty plasma were analyzed both analytically and numerically. The model used included inertialess particles and inertial strongly coupled negatively charged dust grains. Various methods were used to solve the damped nonplanar equations, providing insights into the characteristics of dissipative nonplanar dust-acoustic waves such as solitary and shock waves.
Article
Engineering, Multidisciplinary
Alvaro Humberto Salas Salas, Jairo Ernesto Castillo Hernandez, Lorenzo Julio Martinez Hernandez
Summary: The paper solves the Duffing equation with given initial conditions and introduces the concept of discriminant. It solves the equation in three cases based on the sign of the discriminant and demonstrates its application in soliton theory.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Alvaro H. Salas, Wedad Albalawi, M. R. Alharthi, S. A. El-Tantawy
Summary: This paper introduces novel analytical and numerical techniques for solving and analyzing nonlinear second-order ordinary differential equations. Two different analytical approximations and numerical approximations are presented and applied to real-life nonlinear oscillator equations. The accuracy of these approximations is evaluated through comparisons with the Runge-Kutta numerical approximation.
Article
Mathematics, Interdisciplinary Applications
Haifa A. Alyousef, Alvaro H. Salas, M. R. Alharthi, S. A. El-Tantawy
Summary: In this study, new hypotheses and techniques are presented to obtain new analytical solutions to the generalized Kawahara equation. Traveling wave solutions to both the Kawahara equation and the modified Kawahara equation are derived, with periodic and soliton solutions obtained. The solutions can be applied to the study of nonlinear waves propagating in plasma.
Article
Engineering, Multidisciplinary
Alvaro Salas, H. Lorenzo J. Martinez, R. David L. Ocampo
Summary: In this paper, we demonstrate the application of analytical and numerical techniques to solve the forced Van der Pol oscillator. The obtained results are illustrated through examples and compared with the Runge-Kutta numerical method to assess the accuracy of the approximated analytical solution.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Mathematics
Haifa A. Alyousef, Alvaro H. Salas, Sadah A. Alkhateeb, S. A. El-Tantawy
Summary: This study obtains some exact solutions and approximations to the damped Duffing-Mathieu-type oscillator with cubic nonlinearity. These solutions can help researchers interested in studying the nonlinear oscillations and waves in plasma physics.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Alvaro H. Salas, Lorenzo J. Martinez H, David L. Ocampo R
Summary: This article accurately solves the problem of periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator, provides examples of physical applications, and obtains the solution to the mixed parity Duffing oscillator while high accurate trigonometric approximation to the Jacobian function is given.
Article
Mathematics
Alvaro H. Salas, Wedad Albalawi, S. A. El-Tantawy, L. S. El-Sherif
Summary: In this study, both unforced and forced Duffing-Van der Pol oscillators with a strong nonlinearity and periodic excitations are analyzed using new and improved methods. The new method based on the Krylov-Bogoliubov-Metroolsky method shows the advantage of solving algebraic equations instead of differential equations, providing accurate results more efficiently. The He's frequency-amplitude formulation is also improved to obtain high-accuracy results for unforced oscillators. The comparison of different approaches demonstrates the superiority of the proposed method, which can be applied to analyze higher-order nonlinearity oscillators and give more accurate results.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
M. R. Alharthi, Alvaro H. Salas, Wedad Albalawi, S. A. El-Tantawy
Summary: Novel approximate analytical and numerical solutions to the forced damped driven nonlinear pendulum equation and relation equations on the pivot vertically were obtained, aiding in understanding various phenomena related to plasma physics, classical mechanics, quantum mechanics, optical fiber, and electronic circuits.
JOURNAL OF MATHEMATICS
(2022)
Article
Mechanics
Haifa A. Alyousef, Alvaro H. Salas, R. T. Matoog, S. A. El-Tantawy
Summary: This study presents a detailed investigation on the completely non-integrable forced damped Gardner/Extended Kawahara equation (FDEKE) and proposes three techniques to approximate the equation. The properties of periodic forced dissipative extended Kawahara solitary and cnoidal waves are analyzed numerically and analytically, and the accuracy of the obtained approximations is evaluated. The study highlights the potential applications of these approximations in various fields.
Article
Nanoscience & Nanotechnology
Weaam Alhejaili, Alvaro H. Salas, S. A. El-Tantawy
Summary: Motivated by theoretical investigations, this study analyzes and discusses nonlinear plasma oscillations based on the generalized Van der Pol equation and the two-fluid model. Two analytical approaches, the ansatz method and the Krylov-Bogoliubov-Mitropolsky (KBM) technique, are used to derive approximations, which are compared with the numerical approximation obtained using the Runge-Kutta method. The distance error between the obtained approximations and the RK numerical approximation is also estimated. The proposed methods and approximations can contribute to the study of nonlinear oscillations in various plasma models and fluid mechanics.
Article
Mathematics
Weaam Alhejaili, Alvaro H. Salas, S. A. El-Tantawy
Summary: This study examines the damped parametric driven nonlinear pendulum equation/oscillator, along with associated oscillators for arbitrary angles with the vertical pivot. The pendulum equation is reduced to the damped Duffing equation with variable coefficients for analysis and solution. Two analytical approximations for the damped undisturbed NPE and three analytical approximations for the damped disturbed NPE are obtained using different methods, and their solutions are compared with 4th-order Runge-Kutta approximations. The proposed approaches and solutions are helpful in understanding nonlinear phenomena in various scientific fields.
JOURNAL OF MATHEMATICS
(2023)
