1) high-order subsidiary ordinary differential equation(sub-ODE)
高次辅助方程
1.
With the aid of homogeneous balance principal and a high-order subsidiary ordinary differential equation(sub-ODE),the exact solutions(including the hyperbolic type solitary wave,the sinusoidal traveling wave and the algebraic solitary wave) of the generalized Hamilton Amplitude equation with a high-order nonlinear term are derived.
借助于齐次平衡原则和一高次辅助方程,研究了广义哈密顿振幅方程,求出了该方程的双曲函数、三角函数及代数形式的精确解。
2) high order auxiliary function
高阶辅助方程
1.
We have obtained some new exact travelling wave solutions of the coupled modified Kadomtsev-Petviashvili equations by using the travelling wave transform and a high order auxiliary function and the Jacobi elliptic function periodic solutions.
考虑耦合修正Kadomtsev-Petviashvili(CMKP)方程的行波解,通过一个适当的变换,将耦合修正Kadomtsev-Petviashvili(CMKP)方程转化为一个同解方程,然后对该方程进行波变化,把求偏微分方程问题转为求解常微分方程,通过引进高阶辅助方程,利用Jacobi椭圆函数,取得了CMKP方程的一些新的精确行波解。
3) height aiding
高程辅助
1.
On the basis of modeling of 3D digital map,a lane-level positioning method was presented based on virtual differential GPS with single GPS receiver,height aiding,and collision detecting technique.
在对三维电子地图建模的基础上,提出了一种基于单GPS的虚拟差分、高程辅助定位和碰撞检测误差消除相结合的车道级车辆定位方法。
4) auxiliary equation
辅助方程
1.
The auxiliary equation for constructing the exact solutions of the variable coefficient combined KdV equation with forcible term;
辅助方程构造带强迫项变系数组合KdV方程的精确解
2.
The auxiliary equation for constructing the exact solutions of coupled KdV equations
辅助方程构造耦合KdV方程组的精确解
3.
Global asymptotic stability of a class of nonlinear rational difference equations was studied by means of setting up an auxiliary equation,so that a sufficient condition was obtained.
运用建立辅助方程的方法研究一类非线性有理差分方程正平衡点的全局渐近稳定性,得到一个充分条件。
5) auxiliary equation method
辅助方程
1.
In this paper,we make use of extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics,we obtain some new periodic wave solutions for Klein-Gordon equation which can not be found by previous work.
运用映射法,结合辅助方程,利用计算机代数系统Mathematica求出了非线性Klein-Gordon方程的一系列新的精确周期解,补充了前面研究的结果。
2.
In this paper,we make use of extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics,we obtain some new periodic wave solutions for mKdV and Klein-Gordon equation which can not be found by previous work.
本文运用映射法,结合辅助方程,利用计算机代数系统Mathematica求出了典型的非线性mKdV方程和Klein-Gordon方程的一系列新的精确周期解。
3.
In this work,2D cubic-quintic Ginzburg-Landau equation with diffractive-diffusive terms and normal dispersion is considered,some new exact traveling wave solution are obtained successfully by using identical reforming of differential equation method combine with a new auxiliary equation method.
利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解。
6) auxiliary equation method
辅助方程法
1.
The history and current situation of the auxiliary equation method to search for exact solutions of nonlinear evolution equations by symbolic computing systems are summarized.
综述了基于符号计算寻找非线性发展方程(组)精确解的辅助方程法研究的历史和现状。
2.
According to the characteristics of this equation,using the auxiliary equation method,an auxiliary nonlinearly ordinary equation with high term is constructed.
根据这个广义Boussineq方程的特点,利用辅助方程法构造了一个非线性高次常微分辅助方程,再通过映射的方法,由辅助方程的解获得了广义Boussineq方程的各种精确解的解析表达式。
3.
In this paper,with the help of the software Mathematica,many new exact solutions of generalized fifth-order KdV equation are obtained by using auxiliary equation method.
本文运用辅助方程法,借助Mathematica软件,获得了一类广义五阶KdV方程的19个精确解,其中有17个是新得到的,这些解包括光滑孤立波解,爆破解,周期爆破解。
补充资料：二阶线性齐次微分方程
二阶线性微分方程的一般形式为
ay"+by'+cy=f(1)
其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0，则方程（1）变为
ay"+by'+cy=0（2）
称为二阶线性齐次微分方程，而方程（1）称为二阶线性非齐次微分方程。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条