BOUSSINESQ方程初边值问题的孤立波解

本文给出了Boussinesq方程的一种差分格式并对其初边值问题进行了数值模拟。数值证明了在一些边界条件下Boussinesq方程孤立波解的存在。     

爱因斯坦方程的一组严格的双孤立波解

由一个对角型的度规出发,给出了一组严格的引力双孤立波解。这组解是处处正则和稳定的,它们描写两个分别沿正z方向和负z方向的光速传播的孤立波,而且在彼此碰撞后不会改变自己形状并继续传播,文章最后还讨论了这组解相应的时空奇异性和能量正定性问题。 关键词：     

BBM方程和修正的BBM方程新的精确孤立波解

采用一种双曲函数假设和一类新的辅助常微分方程相结合的方法给出BBM方程和修正的BBM 方程新的精确孤立波解.这种方法也可用于寻找其他非线性发展方程新的孤立波解. 关键词： 辅助方程 双曲函数假设 孤立波解     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

Degasperis-Procesi 方程的无穷序列尖峰孤立波解

本文为了构造非线性发展方程的无穷序列尖峰精确解,给出了Riccati方程的Bäcklund 变换和解的非线性叠加公式,并借助符号计算系统Mathematica,用Degasperis-Procesi方程为应用实例,构造了无穷序列尖峰孤立波解和无穷序列尖峰周期解. 关键词： Riccati方程 解的非线性叠加公式 尖峰孤立波解 Degasperis-Procesi 方程     

一类非线性色散Boussinesq方程的隐式孤立波解

用动力系统分岔方法研究了一类非线性色散Boussinesq方程.在不同的参数条件下,给出了该方程具有隐函数形式的孤立波解的解析表达式.数值模拟进一步验证了所得结果的正确性.     

高维非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了修正的Kadomtsev-Petviashvili方程, 得到了它的近似孤立波解, 该解与精确解符合得非常好.结果表明，同伦分析法在求解高维非线性演化方程的孤立波解时, 仍然是一种行之有效的方法. 关键词： 同伦分析法 修正的Kadomtsev-Petviashvili方程 孤立波解     

孤立波演示实验的改进

对孤立子做一个简单明了的介绍,指出孤立波的特殊性质,根据其特殊性质。提出了孤立波演示的改进设想,设计了新的演示装置。     

一种演示正弦-高登方程孤立波的新方法

正弦-高登方程对应的孤立波在非线性物理学中占有重要地位,但它不像孤立水波那样容易产生,它通常发生在微观领域.本文通过一种宏观装置近似演示正弦-高登方程孤立波,在理论上证实了该波为孤立波,研究了该孤立波的稳定发生、波速与碰撞等方面的性质.     

扩散方程的守恒型并行计算格式

辐射流体力学实际问题计算中扩散方程的计算量极大,必须采用并行计算.研究易于在并行机上实施的高效的并行计算方法,通过采用预估修正等多种方式,构造和发展既保持隐式格式的守恒性、同时能保持所需精度与无条件稳定性的并行计算格式,以满足大规模数值求解辐射流体力学问题的需求.     

Soliton Solutions to Coupled Integrable Dispersionless Equations

In this paper, by introducing a new transformation, the bilinear form of the coupled integrable dispersionless (CID) equations is derived. It will be shown that this bilinear form is easier to perform the standard Hirota process. One-, two-, and three-soliton solutions are presented. Furthermore, the N-soliton solutions are derived.     

Soliton Solutions to Coupled Integrable Dispersionless Equations

In this paper, by introducing a new transformation, the bilinear form of the coupled integrable dispersionless （CID） equations is derived. It will be shown that this bilineax form is easier to perform the standard Hirota process. One-, two-, and three-soliton solutions are presented. Furthermore, the N-soliton solutions axe derived.     

Multiple Soliton Solutions of the High Order Broer-Kaup Equations

Using the extended homogeneous balance method, which is very concise and primary, we find the multiple soliton solutions of the high order Broer-Kaup equations. The method can be generalized to dealing with high-dimensional Broer-Kaup equations and other class of nonlinear equations.     

Conservation Laws and Analytic Soliton Solutions for Coupled Integrable Dispersionless Equations with Symbolic Computation

Under investigation in this paper are two coupled integrable dispersionless （CID） equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagation characteristics and interaction behaviors of the solitons are analyzed graphically.     

Conservation Laws and Analytic Soliton Solutions for Coupled Integrable Dispersionless Equations with Symbolic Computation

Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagationcharacteristics and interaction behaviors of the solitons are analyzed graphically.     

Analytical Investigation of Soliton Solutions to Three Quantum Zakharov-Kuznetsov Equations

In the present paper, the two-dimensional quantum Zakharov-Kuznetsov (QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations.     

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.     

New Weierstrass Semi-rational Expansion Method to Doubly Periodic Solutions of Soliton Equations

Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.     

A New Three-Dimensional Lie Algebra and a Modified AKNS Hierarchy of Soliton Equations

A new three-dimensional Lie algebra and its corresponding loop algebra are constructed, from which a modified AKNS soliton-equation hierarchy is obtained.