共查询到19条相似文献,搜索用时 62 毫秒
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为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解.
关键词:
sine-Gordon型方程
解的非线性叠加公式
辅助方程
无穷序列精确解 相似文献
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利用一种推广的代数方法,求解了一类广义Boussinesq方程(B(m,n)方程)和Boussinesq-Burgers方程(B-B方程).获得了其多种形式的显式精确解,包括孤波解、三角函数解、有理函数解、Jacobi椭圆函数周期解和Weierstrass椭圆函数周期解,进一步丰富了这两类方程的解.
关键词:
Boussinesq方程
Boussinesq-Burgers方程
推广的代数方法
显式精确解 相似文献
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本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)ut=(g(x)D(u)ux)x+h(x)P(u)ux+q(x)Q(u)进行研究. 当扩散项D(u)取um (m≠-1,0,1)和eu两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解.
关键词:
广义条件对称
精确解
非线性反应扩散方程 相似文献
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HUANG Ye-Hui WU Hong-Xia XIE Xi ZENG Yun-Bo 《理论物理通讯》2008,49(5):1091-1100
The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS. 相似文献
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Zhengyan Wang 《Physics letters. A》2008,372(9):1435-1439
The derivative versions of Toda equation are produced from the Lax triad composed of the Kaup-Newell and negative Kaup-Newell spectral problems and a new discrete eigenvalue problem. With the help of decomposition and the Darboux transformation, explicit solutions of these derivative Toda equations are obtained. 相似文献
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《Physics letters. A》2014,378(28-29):1925-1931
We show that the discrete Kadomtsev–Petviashvili (KP) equation with sources obtained recently by the “source generalization” method can be incorporated into the squared eigenfunction symmetry extension procedure. Moreover, using the known correspondence between Darboux-type transformations and additional independent variables, we demonstrate that the equation with sources can be derived from Hirota's discrete KP equations but in a space of higher dimension. In this way we uncover the origin of the source terms as coming from multidimensional consistency of the Hirota system itself. 相似文献
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In this paper, we present a combination method of constructing the
explicit and exact solutions of nonlinear partial differential
equations. And as an illustrative example, we apply the method to
the Benney-Kawahara-Lin equation and derive its many explicit and
exact solutions which are all new solutions. 相似文献
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<正>A new coupled integrable dispersionless equation is presented by considering a spectral problem.A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems.As an application,the N-soliton solution of the coupled integrable dispersionless equation is explicitly given. 相似文献
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An attempt is made to study the interaction Hamiltonian,H
int =Gψ
2(x)U(φ(x)) in the Bethe-Salpeter framework for the confined states of theψ particles interactingvia the exchange of theU field, whereU(φ) = cos (gφ). An approximate solution of the eigenvalue problem is obtained in the instantaneous approximation by projecting the Wick-rotated
Bethe-Salpeter equation onto the surface of a four-dimensional sphere and employing Hecke’s theorem in the weak-binding limit.
We find that the spectrum of energies for the confined states,E =2m+B (B is the binding energy), is characterized byE ∼n
6, wheren is the principal quantum number. 相似文献