Chapter 4 gives hyperbolic function transformation method and its applications 第四章討論了雙曲函數(shù)變法及其應(yīng)用
Extended hyperbolic function method and new exact solitary wave solutions of zakharov equations 方程組的新精確孤立波解
Arc hyperbolic function 反雙曲函數(shù)
Modified hyperbolic function method and exact solutions to nonlinear evolution equations 修正雙曲函數(shù)法與非線性發(fā)展方程的精確解
At last , we construct hyperbolic polynomial curves in the space of hyperbolic functions . we call them as hc - bezier curves 文章最后運(yùn)用同樣的方法在雙曲函數(shù)空間中構(gòu)造了hc - b zier曲線。
A general class of solutions to nonlinear scalar equations with static cylindrical symmetry is obtained in the form of a hyperbolic function series . these solutions can be used to describe a long . straight global string 利用雙曲函數(shù)級數(shù)的技術(shù),研究了靜態(tài)軸對稱非線性標(biāo)量方程的解析解.在物理上.這些解描述了無限長的直整體弦
Spline curves defined in the space constructed by polynomial and hyperbolic functions are studied in this paper . the main research contents and achievements are as follow : firstly , we generate the cardinal extended complete chebychevian ( ect ) - systems on the space constructed by polynomial and hyperbolic functions , then introduce the algebraic - hyperbolic b - spline space and identify the dimension law and zero properties . the existence of a basis of splines with minimal compact supports is demonstrated , and functions named non - uniform algebraic - hyperbolic b - splines are obtained by solving certain linear equations with a block matrix 本文主要研究定義在多項(xiàng)式和雙曲函數(shù)構(gòu)成的空間上的樣條曲線,其內(nèi)容和完成結(jié)果如下:一、生成由多項(xiàng)式和雙曲函數(shù)構(gòu)成的空間上的一組典范式ect ( extendedcompletechebychevian )組及其對偶, ,證明非均勻代數(shù)雙曲b樣條空間的維數(shù)定理和零點(diǎn)定理,直接通過解塊矩陣線性方程組得到具有最小緊支撐的非均勻代數(shù)雙曲b樣條函數(shù),進(jìn)而構(gòu)造非均勻代數(shù)雙曲b樣條曲線,還具體給出低階的表示
In section 1 , some nonlinear wave equations of this part discussing are recommended ; in section 2 , the elementary tool of this part utilizing is mentioned , namely , the hyperbolic function method ; in section 3 , seme exact solitary wave solutions to these nonlinear wave equations are attained 本部分由三節(jié)組成,第一節(jié)介紹了所討論的幾類非線性波動方程;第二節(jié)介紹了本部分所使用的基本工具,即,雙曲函數(shù)方法;第三節(jié)給出了這些非線性波動方程的若干精確孤立波解。
The mostly conclusion of this part is as follows , on the conditon of travelling wave , the exact solitary wave solutions to some nonlinear wave equations such as sawada - kotera equation , kaup - kupershmidt equation , the fifth order kdv equation , fisher - kolmogorov equation , on the help of the computer algebraic system ( maple ) , are explicitly established by making use of the hyperbolic function method . this part is maken up of three sections 本部分的主要結(jié)論如下,利用雙曲函數(shù)展開法,在行波條件下,對sawada - kotera方程, kaup - kupershmidt方程,五階kdv方程, fisher - kolmogorov方程,等幾類非線性波動方程求解,將其孤立波表示為雙曲函數(shù)的多項(xiàng)式,從而將非線性波方程的求解問題轉(zhuǎn)化為非線性代數(shù)方程組的求解問題,并借助于計算機(jī)代數(shù)系統(tǒng)求解非線性代數(shù)方程組,最終獲得了這些非線性波動方程的若干精確孤立波解。
The mathematics - mechanization method is applied the field of differential equations . many algorithm for constructing solitary wave solutions for a class of nonlinear wave equations are given , and implemented in a computer algebraic system , such as the hyperbolic tangent function method and the hyperbolic function method etc . exact solitary wave solutions of a great deal of nonlinear equations are gained 將機(jī)械化數(shù)學(xué)方法應(yīng)用于偏微分方程領(lǐng)域,建立了構(gòu)造一類非線性波方程的精確孤立波解的許多算法,如,雙曲正切函數(shù)展開法,雙曲函數(shù)方法等,并在計算機(jī)數(shù)學(xué)系統(tǒng)上加以實(shí)現(xiàn),因而推導(dǎo)出了一批非線性波方程的精確孤立波解。