Investigation of Riemann wave propagating for the variable coefficients complicated 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.

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

International Journal of Scientific Research and Management ◽

10.18535/ijsrm/v6i6.m01 ◽

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 ◽

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.

Nonlinear Physical Phenomena

10.1142/0945 ◽

1990 ◽

Keyword(s):

Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena

AIP Advances ◽

10.1063/1.4895910 ◽

2014 ◽

Vol 4 (9) ◽

pp. 097120 ◽

Cited By ~ 14

Author(s):

A. K. Gupta ◽

S. Saha Ray

Keyword(s):

Traveling Wave ◽

Wave Solution ◽

Traveling Wave Solution ◽

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0172 ◽

2015 ◽

Vol 70 (8) ◽

pp. 669-672 ◽

Cited By ~ 6

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 ◽

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.

A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schr¨Odinger Equation with Variable Coefficients

Zeitschrift für Naturforschung A ◽

10.1515/zna-2005-11-1202 ◽

2005 ◽

Vol 60 (11-12) ◽

pp. 768-774 ◽

Cited By ~ 3

Author(s):

Biao Li ◽

Yong Chen

Keyword(s):

Analytical Solutions ◽

Bäcklund Transformation ◽

Variable Coefficients ◽

Backlund Transformation ◽

Exact Analytical Solutions ◽

Interaction Of Solitons ◽

Varying Dispersion ◽

Physical Phenomena ◽

Truncated Painlevé Expansion ◽

Singular Soliton

By using the truncated Painlevé expansion analysis an auto-Bäcklund transformation is found for the nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Bäcklund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg

Investigation of the effect of nonlinear physical phenomena on charge carrier transport in semiconductor devices

Solid-State Electronics ◽

10.1016/0038-1101(87)90215-2 ◽

1987 ◽

Vol 30 (6) ◽

pp. 579-585 ◽

Cited By ~ 94

Author(s):

T.T. Mnatsakanov ◽

I.L. Rostovtsev ◽

N.I. Philatov

Keyword(s):

Charge Carrier ◽

Carrier Transport ◽

Semiconductor Devices ◽

Charge Carrier Transport ◽

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

Mathematical Problems in Engineering ◽

10.1155/2015/871635 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 10

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 ◽

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.

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

Mathematics ◽

10.3390/math9080801 ◽

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 ◽

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).