Uniformly constructing combinatorial solutions, combining a rational function with hyperbolic or trigonometric functions, for the (2+1) dimensional Broer–Kaup–Kupershmidt equation

Qing Liu; Zi-Hua Wang

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Uniformly constructing combinatorial solutions, combining a rational function with hyperbolic or trigonometric functions, for the (2+1) dimensional Broer–Kaup–Kupershmidt equation

机译：（2 + 1）维Broer-Kaup-Kupershmidt方程的构造均匀的组合解，将有理函数与双曲或三角函数组合

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According to two dependent rational solutions to a generalized Riccati equation together with the equation itself, a rational-exponent solution to a nonlinear partial differential equation can be constructed. By selecting different parameter values in the rational-exponent solution, many families of combinatorial solutions combined with a rational function such as hyperbolic functions or trigonometric functions, are rapidly derived. This method is applied to the Whitham–Broer–Kaup equation and a series of combinatorial solutions are obtained, showing that this method is a more concise and efficient approach and can uniformly construct many types of combined solutions to nonlinear partial differential equations.

机译：根据广义Riccati方程的两个从属有理解及其方程本身，可以构造非线性偏微分方程的有理指数解。通过在有理指数解中选择不同的参数值，可以快速导出与有理函数（例如双曲函数或三角函数）组合的组合解的许多族。将该方法应用于Whitham-Broer-Kaup方程，得到了一系列组合解，表明该方法是一种更为简洁有效的方法，可以统一构造非线性偏微分方程的多种组合解。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2010年第6期|共6页
作者
Qing Liu; Zi-Hua Wang;
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正文语种 eng
中图分类物理学;
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1. Uniformly constructing combinatorial solutions, combining a rational function with hyperbolic or trigonometric functions, for the (2+1) dimensional Broer–Kaup–Kupershmidt equation [J] . Qing Liu, Zi-Hua Wang Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2010,第6期

机译：（2 + 1）维Broer-Kaup-Kupershmidt方程的构造均匀的组合解，将有理函数与双曲或三角函数组合
2. New travelling wave solutions for combined KdV—mKdV equation and (2+1)-dimensional Broer—Kaup—Kupershmidt system [J] . Yang Xian-Lin, Tang Jia-Shi Chinese physics . 2007,第2期

机译：组合KdV-mKdV方程和（2 + 1）维Broer-Kaup-Kupershmidt系统的新行波解
3. New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer-Kaup-Kupershmidt system [J] . Yang Xian-Lin, Tang Jia-Shi 中国物理：英文版 . 2007,第002期

机译：组合KdV-mKdV方程和（2 + 1）维Broer-Kaup-Kupershmidt系统的新行波解
4. Symmetry groups and new exact solutions of (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system [C] . Qingqing Yuan, Ya Lei International Conference on Multimedia Technology . 2011

机译：对称组和（2 + 1）的新精确解决方案 - Dimensional Broer-Kaup-Kupershmidt（BKK）系统
5. Order of uniform approximation to analytic functions by rational trigonometric and weighted rational functions. [D] . Simmons, Richard D. 1989

机译：有理三角函数和加权有理函数对解析函数的均匀近似阶数。
6. Some New Traveling Wave Exact Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equations [O] . Jian-ming Qi, Fu Zhang, Wen-jun Yuan, -1

机译：（2 + 1）维Boiti-Leon-Pempinelli方程的一些新的行波精确解
7. The Modified Trial Equation Method To The (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation and Kolmogorov-Petrovskii-Piskunov Equation [O] . Şeyma TÜLÜCE DEMİRAY, Serife DUMAN 2021

机译：修改的试验方程方法（2 + 1） - 二维伯雷 - kaup-kupershmidt方程和kolmogorov-petrovskii-piskunov方程

Uniformly constructing combinatorial solutions, combining a rational function with hyperbolic or trigonometric functions, for the (2+1) dimensional Broer–Kaup–Kupershmidt equation

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