经典和分数阶KP-Burger方程及耦合KdV方程的解析解
Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation
摘要：
非线性偏微分方程（包括经典方程和分数阶方程）解析解的求解是应用数学中一个新兴的课题，因为它在物理、生物和社会科学中有着广泛的应用。本文用广义Tanh方法求KP-Burger方程和耦合KdV方程的精确解。用分数阶子方程法求解分数阶KP-Burger方程和分数阶耦合KdV方程。当分数阶导数的阶数趋于1时，分数阶子方程方法得到的精确解退化为经典解。最后进行了数值模拟。数值模拟表明，当导数阶数趋于1时，两个分数阶微分方程的解分别化为KP-Burger方程的激波解和耦合KdV方程的孤子解.
英文摘要：
Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The exact solution obtained by fractional sub-equation method reduces to classical solution when order of fractional derivative tends to one. Finally numerical simulation has done. The numerical simulation justifies that the solutions of two fractional differential equations reduces to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when order of derivative tends to one.
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