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Pure Mathematics 2025
时间分数阶BBM-Burger方程的新精确解
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Abstract:
基于保形分数阶微积分的定义及性质，通过分数阶行波变换，将分数阶BBM-Burger方程简化为一个非线性常微分方程。然后利用三次多项式的完全判别系统法得到了该方程的三角函数解、有理函数解、雅可比椭圆函数解和双曲函数解等四种形式的精确解，其中雅可比椭圆函数解为新解。
Based on the definition and properties of conformal fractional calculus, the fractional BBM-Burger equation is simplified to a nonlinear ordinary differential equation by fractional travelling wave transformation. Then by using the complete discriminant system method of cubic polynomials, the exact solutions of trigonometric function, rational function, Jacobi elliptic function and hyperbolic function are obtained, among which the Jacobi elliptic function is a new solution.
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