具五次强非线性项的Lienard方程的新精确解
New Exact Solutions of the Lienerd Equationswith Fifth-Order Stronger Nonlinear Terms
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摘要: 通过构造辅助方程,求出了具五次强非线性项的Lienard方程的多种新精确解,包括孤波解、三角函数 解、Jacobi椭圆函数解.利用所得结果可以求出Kundu方程、导数Schr dinger方程和力学中重要的具五次强非线 性项的波方程以及PC方程等重要非线性发展方程的精确解.
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关键词:
- Lienard方程 /
- 孤波解 /
- 三角函数解 /
- Jacobi椭圆函数解
Abstract: By constructing auxiliary differential equations, newmultiple exactsolutions of the Lienard equations with fifth-order stronger nonlinear terms were obtained, including solitary solutions, trigonometric function solutions, Jacobian elliptic function solutions. By use of the results , new multiple explicit exact solutions ofmany important nonlinear evolution equations, such as the Kundu equations, the differential Schr dinger equations, the nonlinear wave equations in mechanics, PC equations and so on, can be solved.
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