Numerical solution of kleinsinegordon equations by spectral method coupled. Consider the onedimensional sinegordon nonlinear hyperbolic equation 1. Blue waters undergraduate petascale education program. Legendre spectral element method for solving sinegordon. Extended capabilities tall arrays calculate with arrays that have more rows than fit in memory. We propose a method to deal with the general sine gordon equation. The fractional sinegordon equation is considered as an interpolation between the classical sinegordon equation corresponding to. On multisoliton solutions of the sinegordon equation in. Compared with previous solutions, our solutions are more general than some of the previous. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sine gordon equation.
Dehghan and shokri solved a onedimensional sinegordon equation using collocation points and approximating the solution using thin plate splines radial basis function. Derivation of the explicit scheme formula for the sine gordon system. Numerical solution of nonlinear sinegordon equation by. The method is based on collocation of modified cubic bsplines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range.
Numerical simulation of the solution to the sinegordon equation on the whole real axis is considered in this paper. Convert a secondorder differential equation into a system of differential equations that can be solved using the numerical solver ode45 of matlab. Pdf a numerical solution for sinegordon type system. The sine gordon equation has attracted wide attention over the years in the description of classical and quantum mechanical phenomena 19, and within the framework of quantumfield theory 917. In this paper, numerical solutions of the secondorder twodimensional sinegordon equation obtained by polynomial differential quadrature method have been discussed. Discrete sine gordon dynamics on networks, submitted, 2016.
I am curious if your original equationfunction that you are trying to plot is yt25 sin3 t. We focus, in particular, on two of their principal solutions, namely the kinklike heteroclinic connections and the timeperiodic, exponentially localized in space breather waveforms. Legendre spectral element method for solving sinegordon equation. Of particular interest is the domain wall collision to 2d sine gordon equation which to the authors knowledge have not been presented in the literature. For real values of x in the interval 1, 1, asindx returns values in the interval 90, 90. In this paper, we propose a numerical scheme to solve the twodimensional dampedundamped sinegordon. Our computations were performed using matlab 7 software on a pentium iv.
The given equation is decomposed into a system of equations and. Finding the equation of a line passing 2 points matlab. Of particular interest is the domain wall collision to 2d sinegordon equation which to the authors knowledge have not been presented in the literature. Compute the sine integral function for these numbers. For analytic solutions, use solve, and for numerical solutions, use vpasolve. Numerical solution to the sinegordon equation defined on. The name of the transient version of the sinegordon equation is a play on words on the similar form of the klein gordon equation specify a region. Equations 1 and 2 are actually the solutions to these pdes.
This paper gives three new solutions to solve the 2d sinegordon equation. The nonlinear sinegordon equation arises in various problems in science and engineering. The proposed method provides a reliable technique which is computer oriented if compared with traditional techniques. In this paper, we develop a numerical method for the ndimensional sinegordon equation using differentiation matrices, in the theoretical frame of matrix differential equations our method avoids calculating exponential matrices, is very intuitive and easy to express, and can be implemented without toil in any number of spatial dimensions. Now im confused with the sinegordon theory which is also 2 dimensional like equation 1. Oct 07, 2014 im supposed to generate a 6 seconds long sine wave that has amplitude of 1. Depending on its arguments, sin returns floatingpoint or exact symbolic results. A numerical solution for sine gordon type system slideshare. These solver functions have the flexibility to handle complicated.
Numerical simulation of the ndimensional sinegordon. We study the stability and convergence of the method and show the convergence of our method. All the results are calculated by using the symbolic calculus software matlab 20a and mathematica. This is the range along the abscissa horizontal axis. The three sides of the triangle are named as follows. In this article, were going to explore a number of ways to calculate the sine series without actually using the sine or cosine function. The sinegordon sg equation is a partial differential equation, which is defined as utt. Based on nonlinear spectral analysis, exact nonreflecting boundary conditions are derived at two artificially introduced boundary points. Sinegordon equations, numerical simulation, matlab.
If you do not specify var, the symvar function determines the variable to solve for. In this paper, we study the legendre spectral element method for solving the sine gordon equation in one dimension. Numerical solution of kleingordon and sinegordon equations. Sine integral function for numeric and symbolic arguments. The opposite side is the side opposite to the angle of interest, in this case side a the hypotenuse is the side opposite the right angle, in this. This matlab function returns the sine function of x. To give the clear overview of this method we consider three examples of klein gordon equation and sine gordon equation. This equation is closely related to the fourier series described in fourier series. Numerical solution of kleinsinegordon equations by spectral. In section 5 we also explore the relationship between the lyapunov equations and the sylvester equation and show how their solutions are related to each other in a simple but interesting way. Notes on the sine gordon equation david gablinger january 31, 2007 abstract in this seminar, we will introduce the sine gordon equation, and solve it using a baecklund transfomation. Geometric numerical integration is synonymous with structurepreserving integration of ordinary differential equations. But avoid asking for help, clarification, or responding to other answers. Numerical simulation of the solution to the sine gordon equation on the whole real axis is considered in this paper.
Sine of argument in degrees matlab sind mathworks italia. The numerical examples were calculated using a matlab program. Gnicodes matlab programs for geometric numerical integration. Thanks for contributing an answer to computational science stack exchange. Y asindx returns the inverse sine sin1 of the elements of x in degrees. Problem with a numerical solution of sinegordon like coupled equations in matlab. Modified cubic bspline collocation method is discussed for the numerical solution of onedimensional nonlinear sine gordon equation. For more information on the numerical method and on the interpretation of these results, please, refer to our preprint. These notes, prepared for the durham summer school 2002, are complementary to the monograph of e. Any one has the builtin function for solving sinegordon equation or how can i find it in matlab if any. Computationalengineeringwithmatlabsinegordonsoliton. Is there any function in matlab that accepts coordinates of two points an gives the related linear equation back.
The main difference is that the sum of sines equation includes the phase constant, and does not include a constant intercept term. In the present chapter, we consider two prototypical kleingordon models. Sine of angle, returned as a realvalued or complexvalued scalar, vector, matrix, or nd array of the same size as x. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sinegordon equation. The sinegordon equation is a nonlinear partial differential equation. Firstly, we discretize the equation by legendre spectral element in space and then discretize the time by the secondorder leapfrog method. Open live script gausslaguerre quadrature evaluation points and weights. Sep 03, 2015 newtons method for solving nonlinear systems of algebraic equations. In mathematics, the sine is a trigonometric function of an angle. Notes on the sine gordon equation david gablinger january 31, 2007 abstract in this seminar, we will introduce the sinegordon equation, and solve it using a baecklund transfomation. Numerical simulation of twodimensional sinegordon solitons. Sine gordon equation using the average vector field avf discrete. Newtons method for solving nonlinear systems of algebraic equations.
Contribute to saulwiggincomputational engineeringwithmatlab development by creating an account on github. This code is meant as a supplement to 1, and is an implementation of a moving mesh energy preserving solver for the 1d sinegordon equation using the average vector field avf discrete gradient. I am curious if your original equation function that you are trying to plot is yt25 sin3 t. The equation describes nonlinear waves in elastic media, and it also has applications in relativistic field theory drazin and. Our method avoids calculating exponential matrices, is very intuitive and easy to express, and can be implemented without toil in any number of spatial dimensions. S solve eqn,var solves the equation eqn for the variable var. The representation on solutions of the sinegordon and. Inverse sine in degrees matlab asind mathworks australia. This matlab code solves the classical nonlinear sine gordon equation on graphs. In this paper, we develop a numerical method for the ndimensional sine gordon equation using differentiation matrices, in the theoretical frame of matrix differential equations. The eqworld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations. Instead, use syms to declare variables and replace inputs such as solve 2x 1,x with solve 2x 1,x.
To give the clear overview of this method we consider three examples of kleingordon equation and sinegordon equation. The sine of an acute angle is defined in the context of a right triangle. Discrete singular convolution method for the sinegordon. The name of the transient version of the sinegordon equation is a play on words on the similar form of the klein gordon equation. Solve algebraic equations to get either exact analytic solutions or highprecision numeric solutions.
We propose a method to deal with the general sinegordon equation. Modified cubic bspline collocation method is discussed for the numerical solution of onedimensional nonlinear sinegordon equation. A matlab differentiation matrix suite applied mathematics. Because these numbers are not symbolic objects, sinint returns floatingpoint results. Kaya 7 has implemented the decomposition method for solving the sinegordon equation by using a number of initial values in the form of. Depending on its arguments, sinint returns floatingpoint or exact symbolic results. Now i want to find the linear equation of a line passing through these 2 points. Dehghan and mirzaei used a numerical method of the boundary.
Solve a coupled stationary nonlinear sinegordon equation. The matlab system was used for the numerical computations. Example 1 25 we consider the nonlinear kleingordon equation with, and in the interval with the initial conditions. In this section, we give the basic theory of the sine gordon equation and the variety of its travelingwave solutions, as spatiotemporal models of nonlinear excitations in complex physical systems. Solving an equation containing sine and cosine matlab. The representation on solutions of the sinegordon and klein. Discrete gradient moving mesh solver for the 1d sinegordon equation. Highorder solution of onedimensional sinegordon equation using. The sine function usually expressed in programming code as sinth, where th is an angle in radians is one of the basic functions in trigonometry. A direct method for solving sinegordon type equations request pdf. Also, if you could correct your syntax you might have better luck. Several new exact travelling wave solutions with the form of jacobiamplitude function are derived for the general sine gordon equation by using some reasonable transformation.
Im supposed to generate a 6 seconds long sine wave that has amplitude of 1. In this section, we give the basic theory of the sinegordon equation and the variety of its travelingwave solutions, as spatiotemporal models of nonlinear excitations in complex physical systems. The sinegordon equation has attracted wide attention over the years in the description of classical and quantum mechanical phenomena 19, and within the framework of quantumfield theory 917. In this seminar, we will introduce the sinegordon equation, and solve it. This matlab code solves the classical nonlinear sinegordon equation on graphs. The sinegordon equation firstly appeared in the study of the differential geometry of surfaces with gaussian curvature k.
Sinegordon equation using the average vector field avf discrete. Sine of argument in degrees matlab sind mathworks united. The nonlinear sine gordon equation arises in various problems in science and engineering. This paper gives three new solutions to solve the 2d sine gordon equation. If this is the case, then you need to change your parenthesis so that sin is a function of the independent variable x or t. If this is the case, then you need to change your parenthesis so that sin is a function of the independent variable. If f is a univariate expression or function, then min,max specifies the range for that variable. Sine integral function matlab sinint mathworks india. Adaptive energy preserving methods for partial differential equations. If you do not specify var, the symvar function determines the variable to. New travelling wave solutions for sinegordon equation. Several new exact travelling wave solutions with the form of jacobiamplitude function are derived for the general sinegordon equation by using some reasonable transformation.
Any one has the builtin function for solving sine gordon equation or how can i find it in matlab if any. In this paper, we propose a numerical scheme to solve the twodimensional dampedundamped sine gordon. Support for character vector or string inputs has been removed. Writing a matlab program to solve the advection equation. In this paper, numerical solutions of the secondorder twodimensional sine gordon equation obtained by polynomial differential quadrature method have been discussed. Problem with a numerical solution of sinegordonlike. You can solve algebraic equations, differential equations, and differential algebraic equations daes. Plot symbolic expression, equation, or function matlab. The matlab environment was used for the numerical computations.
Were going to play with the concepts of sine series, iterations, vectorizing programs. Collision of wave packets in the sinegordon equation universiteit. If f is an equation or function of two variables, then min,max specifies the range for both variables, that is the ranges along both the abscissa and the ordinate. Numerical solution of kleinsinegordon equations by. Numerical solution to the sinegordon equation defined on the.
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