scholarly journals Analysis of optical solitons solutions of two nonlinear models using analytical technique

2021 ◽  
Vol 6 (12) ◽  
pp. 13258-13271
Author(s):  
Naeem Ullah ◽  
◽  
Muhammad Imran Asjad ◽  
Azhar Iqbal ◽  
Hamood Ur Rehman ◽  
...  
Keyword(s):  
Nonlinear Models ◽  
Nonlinear Partial Differential Equations ◽  
Optical Solitons ◽  
Nonlinear Dynamical ◽  
Analytical Technique ◽  
The Core ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

<abstract><p>Looking for the exact solutions in the form of optical solitons of nonlinear partial differential equations has become very famous to analyze the core structures of physical phenomena. In this paper, we have constructed some various type of optical solitons solutions for the Kaup-Newell equation (KNE) and Biswas-Arshad equation (BAE) via the generalized Kudryashov method (GKM). The conquered solutions help to understand the dynamic behavior of different physical phenomena. These solutions are specific, novel, correct and may be beneficial for edifying precise nonlinear physical phenomena in nonlinear dynamical schemes. Graphical recreations for some of the acquired solutions are offered.</p></abstract>

scholarly journals Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 129-139 ◽  
Author(s):  
EL Sayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Hyperbolic Function Solutions ◽  
Fibonacci Function

AbstractIn this article, we apply the generalized Kudryashov method for finding exact solutions of three nonlinear partial differential equations (PDEs), namely: the Biswas-Milovic equation with dual-power law nonlinearity; the Zakharov--Kuznetsov equation (ZK(m,n,k)); and the K(m,n) equation with the generalized evolution term. As a result, many analytical exact solutions are obtained including symmetrical Fibonacci function solutions, and hyperbolic function solutions. Physical explanations for certain solutions of the three nonlinear PDEs are obtained.

scholarly journals An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 801
Author(s):  
Md. Nur Alam ◽  
Imran Talib ◽  
Omar Bazighifan ◽  
Dimplekumar N. Chalishajar ◽  
Barakah Almarri
Keyword(s):  
Parabolic Equation ◽  
Mathematical Models ◽  
Exact Solutions ◽  
Analytical Technique ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
Expansion Scheme

In this paper, the adapted (G’/G)-expansion scheme is executed to obtain exact solutions to the fractional Clannish Random Walker’s Parabolic (FCRWP) equation. Some innovative results of the FCRWP equation are gained via the scheme. A diverse variety of exact outcomes are obtained. The proposed procedure could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs).

Numerical solutions of the generalized Rosenau–Kawahara-RLW equation arising in fluid mechanics via B-spline collocation method

2018 ◽  
Vol 29 (11) ◽  
pp. 1850116 ◽  
Author(s):  
Turgut Ak ◽  
Sharanjeet Dhawan ◽  
Bilge İnan
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Wave Interaction ◽  
Spline Collocation ◽  
Nonlinear Dynamical ◽  
Rlw Equation ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
Solitary Wave Interaction

Present study reports the solution of generalized Rosenau–Kawahara-RLW equation. It includes motion of single solitary wave, interaction of two solitary waves along with the calculated invariants and error norms. Gaussian and undular bore initial conditions are studied to show evolution of solitons. Developed train of solitons and conservation of invariants are shown via figures and tables in the respective sections. Various case studies are presented to demonstrate the efficiency of the proposed numerical scheme. Solutions so produced may be helpful for explaining various nonlinear physical phenomena in nonlinear dynamical systems.

scholarly journals New extended generalized Kudryashov method for solving three nonlinear partial differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Reham M.A. Shohib ◽  
Mohamed E.M. Alngar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Nonlinear Partial Differential Equations ◽  
Magnetized Plasma ◽  
Ion Acoustic Waves ◽  
Partial Differential ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
First Time

New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.

DYNAMICAL BEHAVIOR OF q-DEFORMED HENON MAP

2011 ◽  
Vol 21 (05) ◽  
pp. 1349-1356 ◽  
Author(s):  
VINOD PATIDAR ◽  
G. PUROHIT ◽  
K. K. SUD
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Hénon Map ◽  
Chaotic Motions ◽  
Henon Map ◽  
Nonlinear Dynamical ◽  
Complete Deformation ◽  
Nonlinear Maps ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

A recent proposal of q-deformation scheme for the nonlinear maps has stimulated new directions in the studies of various nonlinear dynamical systems. Such studies are advantageous in the analytical modeling of several nonlinear physical phenomena which cannot be perfectly represented by the standard or canonical models. This paper attempts to numerically analyze the behavior of q-deformed version of Henon map, which is one of the prototypical models exhibiting strange chaotic attractor. We particularly investigate the effect of q-deformation on the various kinds of long-term asymptotic dynamics of the canonical Henon map and also characterize the complete deformation parameter space into different regions corresponding to the periodic and strange chaotic motions. We also identify the route to chaos and new structures in the chaotic strange attractor of q-deformed Henon map.

Investigation of Ferroresonance Mitigation Techniques in Voltage Transformer Using ATP-EMTP Simulation

2013 ◽  
Vol 64 (4) ◽  
Author(s):  
Zulkurnain Abdul-Malek ◽  
Kamyar Mehranzamir ◽  
Behnam Salimi ◽  
Hadi Nabipour Afrouzi ◽  
Saeed Vahabi Mashak
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Electrical Equipment ◽  
Resonant Circuit ◽  
Nonlinear Circuit ◽  
Voltage Transformer ◽  
Nonlinear Dynamical ◽  
Electrical Systems ◽  
The Core ◽  
Electrical Phenomenon ◽  
Mitigation Techniques

Ferroresonance is a complex nonlinear electrical phenomenon that can cause dielectric and thermal problems for electrical equipment. Electrical systems with ferroresonant behavior are nonlinear dynamical systems. The ferroresonance phenomenon may take place when the core of an inductive device becomes saturated, and its current flux characteristic becomes nonlinear. While in the case of a linear resonant circuit the resonance frequency is well defined, in the case of a nonlinear circuit, the oscillations may exist at various frequencies, depending on many factors of the particular case. In this paper, ferroresonance phenomenon and its mitigation techniques in 33 kV/110 V voltage transformers (VT) were studied using ATP-EMTP simulation. Initial investigations were carried out for the VT failures occurred at one substation in Malaysia. Physical and burn characteristics of the failed VTs were studied. Simulation results show that ferroresonance cannot be proven to have occurred at the VT due to switching operations since one precondition, namely the critical capacitance, could not have been satisfied. However, in the event of a ferroresonance occurring, several mitigation techniques such as using load resistors, proper grounding sequence, reconfiguration of VT connection, and overcurrent and overvoltage protection can be implemented.

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

scholarly journals A new hybridization filtering-based linear-nonlinear models for time series forecasting

2021 ◽  
Author(s):  
Mehrnaz Ahmadi ◽  
◽  
Mehdi Khashei ◽  
Keyword(s):  
Hybrid Methods ◽  
Nonlinear Models ◽  
Prediction Methods ◽  
Short Term ◽  
Forecasting Methods ◽  
Primary Relationships ◽  
Time Dependencies ◽  
Physical Laws ◽  
Face Time ◽  
Physical Phenomena

In recent years, the idea of using a mathematical model to describe the behavior of physical phenomena has been very much considered. Specifically, a definitive model, based on physical laws, enables researchers to calculate the number of time dependencies precisely at any moment in time. However, in the real world, we often face time-dependent phenomena with many unknown or unavailable factors (Lindley, 2010; Roulston et al., 2003). In this case, when it is not possible to achieve a definite - model, the prediction methods are wide used, especially when the past observations of a variable and primary relationships between specific observations are available. Forecasting methods that are used in different fields of science can be categorized based on various aspects. For example, the prediction methods used in the field of wind energy can be divided into four categories of 1) ultra short term (several seconds to four hours), 2) short term (4 to 24 hours), 3) medium-term (1 to 7 days), and 4) long term (more than 7 days) (Zack, 2003; Soman et al., 2010). Also, the structure of forecasting methods can be divided into two types of 1) single methods and 2) hybrid methods. Each of these categories can also be subdivided into smaller subgroups.

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