In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough （TDB） equation. Since the double exp-function method has been widely used to solve several nonlinear evolution eq...In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough （TDB） equation. Since the double exp-function method has been widely used to solve several nonlinear evolution equations in mathematical physics, we have also used it with the help of symbolic computation for solving the present equation. The method seems to be easier and more accurate thanks to the recent developments in the field of symbolic computation.展开更多
Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their a...Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their affine metrics and affine cubic forms, we construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.展开更多
The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equa...The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The modified tanh-coth function method is easy to execute, brief, efficient, and can be used to solve many other nonlinear evolution equations.展开更多
文摘In this work, it is aimed to find one- and two-soliton solutions to nonlinear Tzitzeica-Dodd-Bullough （TDB） equation. Since the double exp-function method has been widely used to solve several nonlinear evolution equations in mathematical physics, we have also used it with the help of symbolic computation for solving the present equation. The method seems to be easier and more accurate thanks to the recent developments in the field of symbolic computation.
基金supported by the NSF of China(10941002,11001262)the Starting Fund for Distinguished Young Scholars of Wuhan Institute of Physics and Mathematics(O9S6031001)
文摘Hildebrand classified all semi-homogeneous cones in R3 and computed their cor- responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand＇s new examples. After giving their affine metrics and affine cubic forms, we construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.
文摘The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The modified tanh-coth function method is easy to execute, brief, efficient, and can be used to solve many other nonlinear evolution equations.
