scholarly journals Wave Structures for Nonlinear Schrodinger Types Fractional Partial Differential Equations Arise in Physical Sciences

2021 ◽  
Vol 9 (2) ◽  
pp. 101-110
Author(s):  
Mst. Nasrin Nahar ◽  
Md. Tarikul Islam ◽  
Diganta Broto Kar
Keyword(s):  
Partial Differential Equations ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Nonlinear Phenomena ◽  
Partial Differential ◽  
Nonlinear Schrödinger

Nonlinear partial differential equations are mostly renowned for depicting the underlying behavior of nonlinear phenomena relating to the nature of the real world. In this paper, we discuss analytic solutions of fractional-order nonlinear Schrodinger types equations such as the space-time fractional nonlinear Schrodinger equation and the (2+1)-dimensional time-fractional Schrodinger equation. The considered equations are converted into ordinary differential equations with the help of wave variable transformation and then the recently established rational ( )-expansion method is employed to construct the exact solutions. The obtained solutions have appeared in the forms of a trigonometric function, hyperbolic function, and rational function which are compared with those of literature and claimed to be different. The graphical representations of the solutions are finally brought out for their physical appearances. The applied method is seemed to be efficient, concise, and productive which might be used for further research. Mathematics Subject Classifications: 35C08, 35R11

scholarly journals Solusi Persamaan Schrodinger dengan Menggunakan Metode Transformasi Diferensial

2021 ◽  
Vol 4 (1) ◽  
pp. 47
Author(s):  
Muhammad Abdy ◽  
Hisyam Ihsan ◽  
Dhea Ayu Rossyana Dewi
Keyword(s):  
Partial Differential Equations ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Partial Differential ◽  
Differential Transformation ◽  
Initial Values

Abstrak. Penelitian ini membahas tentang solusi persamaan diferensial parsial linier yaitu persamaan Schrodinger. Solusi persamaan ini dilakukan dengan menggunakan metode transformasi diferensial yang merupakan metode semi-numerik-analitik yang dapat digunakan untuk menyelesaikan persamaan diferensial biasa ataupun persamaan diferensial parsial linier dan nonlinier. Metode transformasi diferensial merupakan metode yang menggunakan teori ekspansi deret pangkat pada bentuk transformasinya untuk menentukan solusi. Pada penelitian ini digunakan dua nilai awal pada persamaan Schrodinger yang diberikan. Solusi dengan kedua nilai awal yang diberikan diperoleh dengan menggunakan ekspansi deret Maclaurin. Kemudian solusi tersebut disimulasikan menggunakan software Maple18. Akibatnya, metode transformasi diferensial pada penelitian ini merupakan salah satu metode yang mampu menghasilkan solusi untuk persamaan Schrodinger..Kata Kunci: Persamaan Schrodinger, Metode Transformasi DiferensialAbstract. This study discusses the solution of linear partial differential equations, namely Schrodinger equation. The solution of the equation is done by using the differential transformation method which is a semi-numerical-analytical method, it can be used to solve both ordinary differential equations and linear or nonlinear partial differential equations. Differential transformation method is a method uses the theory of rank expansion in the form of transformation to determine solutions. In this study, two initial values in the given Schrodinger equation were used. Solutions with both initial values given are obtained using the Maclaurin series expansion. Then, the solution is simulated using Maple18 software. As a result, the differential transformation method in this study is one method that is able to solve a solution to the Schrodinger equation.Keywords: Schrodinger Equation, Differential Transformation Method

scholarly journals Newly Developed Analytical Scheme and Its Applications to the Some Nonlinear Partial Differential Equations with the Conformable Derivative

2021 ◽  
Vol 5 (4) ◽  
pp. 238
Author(s):  
Li Yan ◽  
Gulnur Yel ◽  
Ajay Kumar ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rational Function ◽  
Analytical Approach ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Analytical Scheme

This paper presents a novel and general analytical approach: the rational sine-Gordon expansion method and its applications to the nonlinear Gardner and (3+1)-dimensional mKdV-ZK equations including a conformable operator. Some trigonometric, periodic, hyperbolic and rational function solutions are extracted. Physical meanings of these solutions are also presented. After choosing suitable values of the parameters in the results, some simulations are plotted. Strain conditions for valid solutions are also reported in detail.

scholarly journals Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Rational Solutions ◽  
Partial Differential ◽  
Wave Solutions

We apply the G′/G2-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

scholarly journals New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yusuf Pandir ◽  
Halime Ulusoy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
New Exact Solutions

We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

scholarly journals Modeling Nonlinear Partial Differential Equations and Construction of Solitary Wave Solutions in an Inductive Electrical Line

2019 ◽  
pp. 1-10 ◽  
Author(s):  
Tiague Takongmo Guy ◽  
Jean Roger Bogning
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Magnetic Flux ◽  
Differential Equations ◽  
Solitary Waves ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Hyperbolic Function ◽  
Flux Linkage ◽  
Partial Differential

A soliton is considered nowadays as a future wave reason being the fact that it is a stable, robust and non-dissipative solitary wave. If one uses a soliton as a transmission signal in electrical lines, this will have a great impacts in the domain of economic, technology and education. Given the fact that the propagation of the soliton is due to the interaction between dispersion and nonlinearity, it necessitates that the transmission medium should be dispersive and nonlinear. The physical system we have chosen for our survey is an inductive electrical line reason being the fact that it is the cheapest and very easy to manufacture than any other transmission lines; furthermore we find out the analytical variation that the magnetic flux linkage of inductors in the electrical line must undergo so that its transmission medium admits the propagation of solitary waves of required type. The aim of this work is to model nonlinear partial differential equations which govern the dynamics of those solitary waves in the line, to define the analytical expression of the magnetic flux linkage of inductors in the line and to find out some exact solutions of solitary waves types of those equations. To meet our objectives, we apply Kirchhoff laws to the circuit of a nonlinear inductive electrical line to model the nonlinear partial differential equation which describe the dynamics of those solitons. Further we apply the effective and direct Bogning-Djeumen Tchaho-Kofane method based on the identification of basic hyperbolic function coefficients to construct some exact soliton solutions of modeled equations. Numerical simulations have enabled to draw and observe the real profile of those solitary waves which are Kink soliton and Pulse soliton. The obtained results are supposed to permits: The facilitation of the choice of the type of line relative to the type of signal one wishes to send across, to increase the mathematical field knowledge, the reduction of amplification stations of those lines, The manufacturing of new inductors and new electrical lines susceptible of propagating those solitary waves.

Sign in / Sign up

Export Citation Format

Share Document