BİLDİRİ DETAY

Esen HANAÇ
THE PHASE PLANE ANALYSIS OF TRAVELLING WAVE IN NONLINEAR EQUATION
 
I search phase plane analyis for the main results concerning the existence and structure of travelling wave (TWS) which may occur in the large-time solution to the following initial-boundary value problem u_t+kuu_x=cu_xx+u^2 (1-u),-∞0 u(x,0)={( 1, x→-∞ 0, x→∞) u(x,t)→{(1,x→-∞ 0, x→∞) where k≠0 is a parameter. Any solutions to that equation, which is written above, with c>0 supplies travelling wave solution (TWS) that could evolve like the fundamental large time structure in in the solution of the initial-value problem of the diffusion convection reaction equation. . For a specific c which is chosen as depending on parameter k , eigenvalues of the equilibrium points ,these are (0,0) and (1,0), of the jacobian matrix of dynamical system of the equation displays stable point and saddle point. Thus, a heteroclinic orbit is occured from the point which is increasing far from 0 to the point decaying to 0 one, that supports travelling wave solution. Using eigenvalues and eigenvectors of the equilibrium points a general solution is written. After all analytic solutions are done, the phase plane analysis of travelling wave in above equation is drawn by using matlab code which shows all solutions are converged one from to the other.

Anahtar Kelimeler: Diffusion Convection Reaction Equation, Travelling Wave Solution, Stable Unstable Manifolds



 


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