Nonlinear Physical Phenomena

10.1142/0945 ◽  
1990 ◽  
Keyword(s):  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

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.  

Conservation Laws and Soliton Solutions of the (1+1)-Dimensional Modified Improved Boussinesq Equation

2015 ◽  
Vol 70 (8) ◽  
pp. 669-672 ◽  
Author(s):  
Ozkan Guner ◽  
Sait San ◽  
Ahmet Bekir ◽  
Emrullah Yaşar
Keyword(s):  
Conservation Laws ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Ansatz Method ◽  
Nonlocal Conservation Laws ◽  
Dependent Model ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
Evolution Type ◽  
Partial Lagrangian

AbstractIn this work, we consider the (1+1)-dimensional modified improved Boussinesq (IMBq) equation. As the considered equation is of evolution type, no recourse to a Lagrangian formulation is made. However, we showed that by utilising the partial Lagrangian method and multiplier method, one can construct a number of local and nonlocal conservation laws for the IMBq equation. In addition, by using a solitary wave ansatz method, we obtained exact bright soliton solutions for this equation. The parameters of the soliton envelope (amplitude, widths, velocity) were obtained as function of the dependent model coefficients. Note that, it is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.

Multiple explicit solutions of the 2D variable coefficients Chafee–Infante model via a generalized expansion method

2021 ◽  
pp. 2150312
Author(s):  
Rodica Cimpoiasu
Keyword(s):  
Riccati Equation ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Time Variable ◽  
Auxiliary Equation ◽  
Natural Phenomena ◽  
Generalized Riccati Equation ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
First Time

In this work, we do apply a generalized expansion method to the realistic two-dimensional (2D) Chafee–Infante model with time-variable coefficients which is encountered in physical sciences.The key ideas of this method consist in: (i) to choose a nonlinear wave variable in respect to time-variable into the general finite series solution of the governing model; (ii) to take a full advantage from the general elliptic equation introduced as an auxiliary equation which can degenerate into sub-equations such as Riccati equation, the Jacobian elliptic equations, the generalized Riccati equation. Based upon this powerful technique, we successfully construct for the first time several types of non-autonomous solitary waves as well as some non-autonomous triangular solutions, rational or doubly periodic type ones. We investigate the propagation of non-autonomous solitons and we emphasize as well upon the influence of the variable coefficients. We are providing and analyzing a few graphical representations of some specific solutions. The results of this paper will be valuable in the study of nonlinear physical phenomena. The above- mentioned method could be employed to solve other partial differential equations with variable coefficients which describe various complicated natural phenomena.

scholarly journals Analytic Solutions of the Space-Time Fractional Combined KdV-mKdV Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Emad A.-B. Abdel-Salam ◽  
Zeid I. A. Al-Muhiameed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Mapping Method ◽  
Space Time ◽  
Fractional Differential ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
First Time

The fractional mapping method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional combined KdV-mKdV equation. Many types of exact analytical solutions are obtained. The solutions include generalized trigonometric and hyperbolic functions solutions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.

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).

Effect of nonlinear physical phenomena on the photovoltaic effect in silicon p+–n–n+ solar cells

2000 ◽  
Vol 44 (3) ◽  
pp. 383-392 ◽  
Author(s):  
T.T Mnatsakanov ◽  
V.B Shuman ◽  
L.I Pomortseva ◽  
D Schröder ◽  
A Schlögl
Keyword(s):  
Solar Cells ◽  
Photovoltaic Effect ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

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.

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