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李继彬 《应用数学和力学(英文版)》2009,30(5):537-547
Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a "real" loopsolution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions. 相似文献
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对于某些非线性波方程,动力系统方法的分析说明所谓的圈孤子解和反圈孤子解实际上是人为的现象.所谓的圈孤子解由3个解合成,不是1个真解.是否存在非线性波方程,使得该方程的行波系统存在真正的1个圈解?若这样的解存在,它们有怎样的精确参数表示?该文回答这些问题. 相似文献
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应用动力系统理论和方法研究两类广义Boussinesq系统. 在各种参数条件下, 严格地证明了各种可能的光滑和非光滑孤立波解、不可数无穷多周期波解和破缺波解的存在性, 计算了这些解的明显的参数表示, 并确定了这些解存在的参数条件. 相似文献
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李继彬 《应用数学和力学(英文版)》2008,29(11):1391-1398
By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained. 相似文献
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§1.引言 近年来,随着对三维流的吸引集合及浑沌性质研究的深入,关于三维流的扭结周期轨道的研究具有日愈增加的兴趣(见文献[1]等)。1977年,R.Parris与分别给出了同一类型的三阶常微分自治方程,指出该系统存在扭结型周期轨道。1981年,推广文献[2]、[3]的结果,给出了扭结周期轨道存在的一个判定定理。然而文献[2]、[3]所述的系统是可积的,轨道无吸引性,并且对一组固定参数值,该系统只能 相似文献
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本文通过平面复自治系统的规范型研究实系统具有可线性化的中心和鞍点的条件,定义了k-阶广义细中心及其判定量,给出了计算判定量的递推公式,并对三次系统,讨论了周期的临界点分枝问题. 相似文献
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1IntroductionThebrainofmankindhasmanycognitivefunctionssuchaslearning,asociationandoptimizationetc..Theneuronisthemostfoundam... 相似文献
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The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation. 相似文献
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1 Illtroduction and Statement of the Main ResultIn this paper, we shall study the existence of periodic solutions for the twofOllowing differential delay equationsX'(t) = --f(x(t -- r1))g(x(t -- r2)) -- f(x(t -- r2))g(x(t -- r1)), (1)andX'(t) = f(x(t -- rl))g(x(t -- r2)) f(x(t -- r2))g(x(t -- rl)), (2)where ri (i = l,2) are positive constants. When the function g(x) = 1,equations (1) and (2) become respectivelyIn 1974, Kaplan and Yorke (see [101) proved the existence of periodic so1utions… 相似文献