Equation can be written in the real form as follows. In this paper, novel approaches called the modified tanh method are. Travelling wave solution of twodimensional nonlinear kdv. A travelling wave solution of kinktype 2 for the burgerskdv equation is given by ux. It is found that an exact solution of the kdvb equation is obtained by tanhmethod, provided the parameters involved satisfy a constraint relation. It is shown that the solution with the initial disturbance is explicitly represented by virtue of the hopf transformation and tends to a travelling wave solution with the speed depending on. Pdf travelling wave solutions of the burgershuxley equation. Solutions of burgers equation with finite transport memory the sinecosine method 22 and so on. Travelling waves for a nonlocal kdvburgers equation. In this paper, novel approaches called the modified tanh method are used to obtain more generalized travelling wave solution for nonlinear burgers equation. The kortewegde vries and the kortewegde vriesburgers equations are considered. The existence and certain qualitative properties of travellingwave solutions to the kortewegde vriesburgers equation, are established.
Some travelling wave solutions of kdvburgers equation. Isnt it a similar solution, travelling in the other. This paper considers the bounded travelling waves of the rlwburgers equation. We also derive estimates of shock thickness for the nonnewtonian. Travelling wave solutions for a singularly perturbed. The solution 17 of burgers equation is called the shock structure solution because it resembles the actual pro. Travelling wave solutions for the burgers equation and the. New travelling wave solutions of burgers equation with. Travelling wave solution of the fisherkolmogorov equation.
A travelling wave solution to the kdvburgers equation a travelling wave solution to the kdvburgers equation demiray, hilmi 20040715 00. Ablowitz and zeppetella 26 obtained the first explicit form of travelling wave. An attempt has been made to obtain exact analytical travelling wave solution of kortewegde vries burger s kdvb equation by the socalled tanhmethod. A note on the stability of travelling wave solutions of. In the present work, the extended tanh and expfunctionmethodsare used to obtain travelling wave solutions of the timedelayed burgersequationof the form.
Numerical methods for hyperbolic conservation laws 9 6. Moreover, a travelling wave is associated to having a constant velocity throughout its course of propagation. Travelling wave solution consider the nonlinear convectiondi. Notes on burgerss equation maria cameron contents 1. This equation is balance between time evolution, nonlinearity, and di. Some new exact travelling wave solutions in more general form of these two. The solution of the linear wave equation can be obtained as a special case of the nonlinear wave equation 1. Closedform travelling wave solutions to the nonlinear spacetime fractional coupled burgers equation. Wang studied a compound burgers kortewegde vries equation using the homogeneous balance method and obtained a kinkprofile solitary wave solution to eq. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method.
Seeking the travelling wave solution of fisher equation has been a challenging and difficult task. Pdf travelling waves are presented in many different fields of sciences. This was the original inspiration for this study, but not the sole motivation. Travelling wave solution of variablecoefficient burgers equation with variable parameter tanh method. New travelling wave solutions of two nonlinear physical. In this section, we apply the modified simple equation method to find the exact wave solutions and then the solitary wave solutions of the following nonlinear partial differential equations. Travelling wave solutions for the kdvburgerskuramoto and. Can you visualize and understand the travelling wave equation. When these parameters are taking special values, the solitary wave solutions are derived from the. They are shown to be sums of a shock wave and solitary wave.
In the limit, it was shown that the traveling wave solutions of eq. In general, it follows that any solution to the wave equation can be obtained as a superposition of two travelling waves. On new travelling wave solutions of the kdv and the kdv. The new types of wave solutions of the burgers equation and the. Using the travelling wave the general solutions of these equations are presented. What is the difference between equation for wave pulse, periodic wave motion and. For the oscillatory kink wave, the regularity of its maximum oscillation amplitude changing with parameters is discussed. Pdf new travelling wave solutions of burgers equation with. In section 4 we apply the simplest equation method to the kdv equation and obtain all solitary wave solutions from the list by wazzan as well. Exact expressions of the monotone kink waves and approximate. New travelling waves solutions for solving burgers equations by. To illustrate the technique of looking for travelling wave solutions on a simple example.
Abstractin this study, travelling wave solution of variable ent burgers equation is extracted using variablecoeffici parameter tanh method. The stability of travelling wave solutions of burgers equation is investigated. Exact traveling wave solutions of modified kdvzakharov. On traveling wave solutions to modified burgerskorteweg. Some travelling wave solutions of kdvburgers equation 1057 equation 14, we have m 2. It is an example of a traveling wave or wavefront solution. We prove that there only exist two types of bounded travelling waves, the monotone kink waves and the oscillatory kink waves. Therefore, a class of travelling solitary wave solutions with arbitrary velocities is obtained. In section 2, we analyse the stability and bifurcation of system 7, which is equivalent to the 2dbkdv equation 1aftermaking travelling wave transformation and integration. A travelling wave solution to the kdvburgers equation. Emran ali, farjana bilkis, gour chandra paul, hasibun naher, nasir taghizadeh.
It it interesting to explore what happens to traveling waves in burgers equation 1. They had to determine seven parameters to obtain a solu tion. Travelling wave solutions of burgersequation for geelyon. Travelling wave solutions a dissertation submitted to the university of manchester for the degree of master of science in the faculty of science and engineering.
The traveling wave solutions are expressed in terms of the exponential functions, the. Traveling wave solutions of a generalized burgers equation. New travelling waves solutions for solving burger s equations by tancot function method 1. Burgers equation has a s table largetime travelling wave solution and it leads to a g ood prediction of time to ponding during rainfall. Burgers equation, applied mathematics and computationvolume 216, issue 11, pp. New travelling waves solutions for solving burgers. Indeed, weve seen that nonlinear advection equations admit shock solutions that are less smooth than their initial data.
For phase plane analysis the system is linearised around. In the present work, by introducing a new potential function and by using the hyperbolic tangent method and an exponential rational function approach, a travelling wave solution to the kdvburgers kdvb equation is presented. The kdvburgers equation is a nonlinear partid differential equation which arise in the study of many physical problems 1,2. Travelling wave solutions of multisymplectic discretisations of wave equations a thesis presented in partial ful llment of the requirements for the degree of doctor of philosophy in mathematics at massey university, manawatu, new zealand. Now we will find travelling wave solutions for the nls equation. Traveling wave solution 8 of convectiondiffusion equation. Persistence of travelling wave solutions of a fourth order. Request pdf a travelling wave solution to the kdvburgers equation in the present work, by introducing a new potential function and by using the hyperbolic tangent method and an exponential. Travelling wave solutions to the twodimensional kdv. Analytic solutions of the vector burgers equation 67 a simple example of the use of this method is to use the initialvalue solution of the diffusion equation a dirac delta at t r 0 0 6.
As a result, hyperbolic, trigonometric, and rational function solutions with parameters are obtained. On travelling wave solutions of the burgerskortewegde vries equation 345 enable us to reduce equation 1 to three. The obtained solutions are all travelling wave solutions. Travelling wave solution of variablecoefficient burgers.
We assume formal solutions of the form where, are constant parameters to be determined later, and is an arbitrary constant. Travelling wave solutions lor the twodimensional kdvburgers equation are obtained by using mafhemlica. Solution of the burgers equation with nonzero viscosity 1 2. The solutions include the corresponding wellknown traveling wave solution of the burgersequation for newtonian. Some travelling wave solutions of kdvburgers equation 1. From now on, unless indicated otherwise, we will refer to eq. Travelling wave solutions of the burgers huxley equation article pdf available in ima journal of applied mathematics 773 july 2012 with 278 reads how we measure reads. Exact traveling wave solutions of nonlinear pdes in. Pdf new traveling wave solutions of a burgers equation by using.
Burgers equation consider the initialvalue problem for burgers equation, a. Pdf the nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. Closedform travelling wave solutions to the nonlinear. Traveling wave solutions of a generalized burgers equation 625 to solve equation 3. Pdf new traveling wave solutions of a burgers equation.
Travellingwave solutions to the kortewegde vriesburgers. Kink waves and their evolution of the rlwburgers equation. In this article, a generalized g gexpansion method is used to. Equation 2 has a solution in the form of the traveling wave ux. New travelling waves solutions for solving burgers equations by tancot. Travelling wave solutions and proper solutions to the two. It clearly represents a wavefront moving with velocity c. Now we will discuss some of the obtained results of viscous burgers equation and their graphical representations. New travelling wave solutions of the kdv and the kdvburgers equations by wazzan wazzan l commun nonlinear sci numer simulat 2009. In this paper we look for travelling wave solutions of 1, in. Then, the persistence of the travelling wave solution for the. First, the convergence to the uniform steady state is proved, which means the solution of the equation with positive initial data will remain positive for time t suf.
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