Complex-Valued Burgers and KdV-Burgers Equations
نویسندگان
چکیده
Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T , there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T . In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild conditions.
منابع مشابه
The Modified Extended Direct Algebraic Method for Solving Nonlinear Partial Differential Equations
By means of modified extended direct algebraic (MEDA) method the multiple exact complex solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. New complex solutions for nonlinear equations such as one-dimensional Burgers, KDV-Burgers, coupled Burgers and twodimensional Burgers’ equations are obtained.
متن کاملShock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations
Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the timeaveraged patterns for the case of stepwise fixed boundary conditions. Our results show that the shock structure for the noisy KdV-Burgers equation has an oscillating tail, even for the time averaged pattern. Also, we find that the width of the s...
متن کاملSoliton solutions of Burgers equations and perturbed Burgers equation
This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. 2010 Elsevier Inc. All rights reserved.
متن کاملLie Group Method for Solving the Generalized Burgers', Burgers'-KdV and KdV Equations with Time-Dependent Variable Coefficients
In this study, the Lie group method for constructing exact and numerical solutions of the generalized time-dependent variable coefficients Burgers’, Burgers’–KdV, and KdV equations with initial and boundary conditions is presented. Lie group theory is applied to determine symmetry reductions which reduce the nonlinear partial differential equations to ordinary differential equations. The obtain...
متن کاملComplex PT-symmetric nonlinear Schrödinger equation and Burgers equation.
The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Nonlinear Science
دوره 20 شماره
صفحات -
تاریخ انتشار 2010