TY - JOUR T1 - Analysing of Nonlinear Advanced Equation in Dynamic System TT - Dinamik Sistemde İleri Nonlineer Denklemin Analizi AU - Hanaç, Esen PY - 2021 DA - December DO - 10.31590/ejosat.1005848 JF - Avrupa Bilim ve Teknoloji Dergisi JO - EJOSAT PB - Osman SAĞDIÇ WT - DergiPark SN - 2148-2683 SP - 141 EP - 145 IS - 31 LA - en AB - We mainly examine the type of the structure of the solutions of the following equation namely, u_t+kuu_x=u_xx+u^2 (1-u),-∞ KW - Phase-space analysis KW - Nonlinear advanced equation KW - Shock-wave solutions. N2 - Aşağıdaki denklemin u_t+kuu_x=u_xx+u^2 (1-u),-∞ CR - Behzadi, S.S and Araghi, M.A.F., (2011). Numerical Solution for Solving Burgers-Fisher Eguation by Using Iterative Methods.Mathematical and Computational Applications16, 443-455. https://doi.org/10.3390/mca16020443 CR - Bramson, M.D., (1983). Convergence of solutions of the Kolmogorov equation to travellingwaves. Mem. Amer. Math. Soc.44. ISBN: 978-1-4704-0695-0 CR - Burgers, J.M., (1939). Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion.Verh. Nederl. Akad. Wetensch. Afd. Natuurk.17, 1-53. https://www.dwc.knaw.nl/DL/publications/PU00011461.pdf CR - Burgers, J.M., (1940). Application of a model system to illustrate some points of the statistical theory of free turbulence. Proc. Kon. Nederl. Akad. Wetensch.43, 2-12. CR - Burgers, J.M., (1975). The Nonlinear Diffusion Equation. D. Reidel Publishing Company, Dordrecht, Holland. CR - Fisher, RA., (1937). The wave of advance of advantageous genes. Annals of Eugenics. 7 355-369. https://doi.org/10.1111/j.1469-1809.1937.tb02153.x CR - Griffiths, G., Schiesser, W. E., (2009). A Compendium of Partial Differential EquationModels. Cambridge University Press doi:10.1017/CBO9780511576270 CR - Griffiths, G., Schiesser, W. E., (2010). Travelling Wave Analysis of Partial DifferentialEquations. Academic Press. ISBN: 978-0-12-384652-5 CR - Hanaç, E. (2021). The Stability of A modified form of Reaction Diffusion Equation in Phase Plane. https://doi.org/10.31590/ejosat.920615 CR - Kolmogorov, AN, Petrovskii, PG, Piskunov, NS. (1937). A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem. Moscow University Mathematics Bulletin. 1 1-26. CR - Kot, M., (2003). Elements of Mathematical Ecology. Camridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511608520 CR - Landejuela, M., (2011). Burgers Equation. BCAM Internship report: Basque Center forApplied Mathematics. CR - McKean, H.P., (1975) . Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math.28, 323-331. https://doi.org/10.1002/cpa.3160280302 CR - Murray, JD. (2002). Mathematical Biology I: An Introduction. Third edition, Springer, New York. ISBN 978-0-387-22437-4 CR - Van Saarloos, W., (2003). Front propagation into unstable states. Phys. Rep.386, 29-222. UR - https://doi.org/10.31590/ejosat.1005848 L1 - https://dergipark.org.tr/tr/download/article-file/2014058 ER -