Abstract
Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.
Highlights
Exact solutions of nonlinear partial differential equations (NPDEs) have been of a major concern for both mathematicians and physicists [1-4]
In the past few decades, many significant methods have been presented such as Bäklund transformation, Darboux transformation, the extended tanh-function method, and the F-expansion method, Lie group analysis, homogeneous balance method, Jacobi elliptic function method, and the mapping method, etc. [9-15]
Via a mapping equation we find some new non-traveling wave solutions of the (1 + 1)-dimensional Burgers equation: Qt QQx Qxx 0
Summary
Exact solutions of nonlinear partial differential equations (NPDEs) have been of a major concern for both mathematicians and physicists [1-4]. The mapping approach is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations, the remarkable characteristic of which is that we can have many different ansatzs and a large number of solutions. We have solved the exact solutions of some nonlinear sys-. Tems via the Riccati equation 2 mapping method, such as (1 + 1)-dimensional related Schrödinger equation, (2 + 1)-dimensional Generalized Breor-Kaup system, (3 + 1)-dimensional Burgers system, (3 + 1)dimensional Jimbo-Miwa system, (2 + 1)-dimensional modified dispersive water-wave system, (2 + 1)-dimensional Boiti-Leon-Pempinelli system, (2 + 1)-dimensional Korteweg de Vries system, (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system et [16-19]. Via a mapping equation we find some new non-traveling wave solutions of the (1 + 1)-dimensional Burgers equation: Qt QQx Qxx 0
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