CAJ | 학술논문

基于一变系数Riccati方程及其解,在内行波变换和指数变换的辅助下,提出改进的扩展tanh函数方法及其算法.该方法对构造非线性发展方程(组)的精确行波解方面比tanh函数方法和各类扩展tanh函数方法更强劲.以Broer-Kaup方程组和近似长水波方程组为举例,得到包括三角周期波解、孤立波解、复杂波解和有理函数解等丰富有趣的行波解.该方法简洁有效,可适合应用于其它非线性发展方程(组).
기우일변계수Riccati방정급기해,재내행파변환화지수변환적보조하,제출개진적확전tanh함수방법급기산법.해방법대구조비선성발전방정(조)적정학행파해방면비tanh함수방법화각류확전tanh함수방법경강경.이Broer-Kaup방정조화근사장수파방정조위거례,득도포괄삼각주기파해、고립파해、복잡파해화유리함수해등봉부유취적행파해.해방법간길유효,가괄합응용우기타비선성발전방정(조).
Based on a Riccati equation with variable coeficients and its solutions, with the help of an internal travelling wave transformation and an exponential transformation of functions, we present the improved extended tanh function method and its algorithm, which are powerful than the tanh function method and several forms of the extended tanh function method to construct new exact travelling wave solutions of nonlinear differential equations in mathematical physics. Both the Broer-Kaup equations and the approximate long water wave equations are chosen to illustrate our algorithm such that rich interesting travelling wave solutions are obtained, which include the triangular periodic wave solutions, the solitary wave solutions, the complex travelling wave solutions and the rational function solutions. This method is concise and effective, and it can be applied to other nonlinear evolution equations.