| 1. | The new jacobi elliptic function expansion method by the long - short wave interaction equation
椭圆函数新的展开法求解 |
| 2. | Exact periodic solutions with jacobi elliptic functions fractional form to generalized modified boussinesq equation
方程椭圆函数分式形式的精确周期解 |
| 3. | Finally , a chebyshev function bpf with siw resonator was designed and realized by ltcc with 12 - layer substrate . a high performance elliptic function bpf with siw resonator was designed
在分析ltcc集成高q滤波器实验结果的基础上,设计了一个基于siw技术的9层基片的高性能的椭圆函数滤波器。 |
| 4. | By using the modified mapping method and the extended mapping method , we derive some new exact solutions of the higher order nonlinear schr ? dinger equation , which are the linear combination of two different jacobi elliptic functions
摘要通过修正的映射方法和推广的映射方法，我们得到了高阶非线性薛定谔方程新的精确解，它们是两个不同的雅可比椭圆函数的线性组合。 |
| 5. | In this letter , we introduce the rule of the linear and non - linear movement of the single pendulum , and by using the jacobian elliptic function , we educe two categories of movement fuctions of the single pendulum , the results will be some referential improtance in studying the non - linear vibrational systems
摘要介绍了单摆的线性与非线性运动规律，并利用雅可比椭圆函数法导出了单摆作两种运动的方程，对研究非线性振动的系统有一定参考价值。 |
| 6. | ( 2 ) by the jacobi elliptic function expansion method and computer symbolic systems ( maple , matlab ) , many exact periodic solutions of nonlinear wave equations can be obtained and these solutions can degenerate solitary wave solutions , shock wave solutions , trigonometric function solutions
( 2 )利用jacobi椭圆函数表示法和数学计算软件( maple ， matlab等) ，可以得到一类常系数非线性发展方程的双周期解，这些解能退化成孤立子解，冲击波解，三角函数解。 |
| 7. | In the part of discussion , the suitability of the jacobi elliptic function expansion method is also studied by proposing the " rank " . and we firstly point out that when the " ranks " of every term of the nonlinear evolution equation are simultaneously even or odd , the method can be used to solve the equation
为了讨论了jacobi椭圆函数展开法的适用性问题，我们最先引进“秩”的概念，指出只要非线性发展方程的各项的“秩”满足相同的奇偶性，就可以用这种展开法求解。 |
| 8. | Chapter5 : the recently developed method of hyperbolic tangent function expansion is extended and new function transformation is applied to construct some new solitary solutions of kdv equation and klein - gordon equation and the jacobi elliptic function expansion method , which is advanced in 2001 , and the extended method of doubly jacobi function expansion are used to construct the exact solutions of a kind of nonlinear evolution equations
第五章对近年来发展起来的双曲正切函数展开法加以改进，采用新的变换函数，得到了kdv方程和非线性klein - gordon方程的一些新的孤立波解。其次，分别采用2001年提出的jacobi椭圆函数展开法和本文由此扩展而来的双椭圆函数展开法，求解了一大类非线性发展方程，得到了一系列新的周期解。 |
| 9. | We improve this method as follows : ( 1 ) single jacobi elliptic function is replaced with an unified jacobi elliptic equation , thus repeated calculation is avoided ; ( 2 ) extending the expansion method from sole - function to double - function form , the more solutions for npde are obtainted ; ( 3 ) using many of jacobi elliptic functions besides ordinary three kinds , the content of solutions represented by jacobi elliptic by the jacobi elliptic function expansion method and computer functions is very abundant
我们对此方法做了如下几点改进：用统一的jacobi椭圆方程组代替单个的jacobi椭圆函数，避免重复计算；将jacobi椭圆单函数展开方法推广到jacobi椭圆双函数展开，这样可以得到更多的解；将通常使用的三个jacobi椭圆函数推广到多个jacobi椭圆函数，丰富了用jacobi椭圆函数表示的解的内容。利用改进的jacobi椭圆函数展开法，求解了bbm方程和boussinesq方程组。 |
| 10. | ( 2 ) by the jacobi elliptic function expansion method and computer symbolic systems ( maple , matlab or mathematica ) , many exact periodic solutions of nonlinear wave equations can be obtained and under some conditions , these solutions degenerate solitary wave solutions , shock wave solutions , trigonometric function solutions respectively
( 2 )利用jacobi椭圆函数展开法和数学计算软件( maple ， matlab ， mathematica等) ，可以求得一类常系数非线性发展方程的双周期解，这些解能退化成孤立子解、冲击波解、三角函数解。 |
