Abstract
In this paper, we develop the nonlinear integrable couplings of Burgers equations with time-dependent variable coefficients. A new simplified bilinear method is used to obtain new multiple-kink solutions and multiple-singular-kink solutions for this system. The proposed system is a generalization model in ocean dynamics, plasma physics and nonlinear lattice. The effects of time-variable coefficients on the velocity, phase and amplitude are given. The solitonic propagation and collision are discussed by the graphical analysis and characteristic-line method.
Highlights
1 Introduction The classical coupled Burgers equations (CBE) [ – ] with time t and space x derivatives are given by vt – vxx – vvx + a(vw)x =, ( )
We develop the classical coupled Burgers equations ( ) to derive nonlinear n-coupled Burgers equations with time-variable coefficients in the form
We see that the forms of the variable coefficients determine the appearances of the characteristic curve and correspond to distinct propagation trajectories
Summary
The classical coupled Burgers equations (CBE) [ – ] with time t and space x derivatives are given by vt – vxx – vvx + a(vw)x = , ( ). The coupled Burgers equations (CBE) arise in a large number of applications in physics, engineering and mathematical problems. Some if these applications are plasma physics, fluid mechanics, optic, solid state physics, chemical physics, etc. We develop the classical coupled Burgers equations ( ) to derive nonlinear n-coupled Burgers equations with time-variable coefficients (nc-BE) in the form ⎫. Many researchers in applied mathematics give great attention to finding the analytical, approximation and exact solutions of CBE by different methods such as variational iteration method [ ], Adomian-Pade technique [ ], differential transformation method [ ], exponential function method in rational form [ ], homotopy analysis method [ ], modified extended direct algebraic (MEDA) method [ ], first integral method [ ], reduced differential transform method [ ] and the Hirota bilinear method [ ].
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