共查询到10条相似文献,搜索用时 296 毫秒
1.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(5):877-888
The periodic wave solutions and the corresponding solitary solutions for the shallow water equations and the generalized Klein–Gordon equation are obtained by means of mapping method. The solutions obtained in this paper include as well the shock wave solution, complex line period, complex line soliton and rational solutions. Moreover, the obtained solutions are degenerated in terms of hyperbolic function solutions and trigonometric function solutions when the modulus m of the Jacobi elliptic function is driven to 1 and 0, respectively. The previously known periodic and solitary wave solutions are recovered. Many new results are presented. 相似文献
2.
广义组合KdV-mKdV方程的显式精确解 总被引:1,自引:0,他引:1
Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations. 相似文献
3.
《Nonlinear Analysis: Theory, Methods & Applications》2005,61(6):1015-1030
The behavior of a periodically forced, linearly damped mass suspended by a linear spring is well known. In this paper we study the nature of periodic solutions to two nonlinear spring-mass equations; our nonlinear terms are similar to earlier models of motion in suspension bridges. We contrast the multiplicity, bifurcation, and stability of periodic solutions for a piecewise linear and smooth nonlinear restoring force. We find that while many of the qualitative properties are the same for the two models, the nature of the secondary bifurcations (period-doubling and quadrupling) differs significantly. 相似文献
4.
Vladimir Ivanovich Mironenko Vladimir Vladimirovich Mironenko 《Journal of Applied Analysis & Computation》2016,6(3):876-883
In the paper we are giving the new method for searching periodic solutions of periodic differential systems. For this we construct a differential system with the same Reflecting Function as the Reflecting Function of the given system and with a known periodic solution. Then the initial data of the periodic solutions of this two systems coincide. In such a way the problem of existance periodic solutions goes to the Cauchy problem. 相似文献
5.
While the nonlinearities are bounded below, we establish the existence and multiplicity results of doubly periodic solutions for a coupled nonlinear telegraph system with a parameter. The proof is based on a well known fixed theorem in a cone. 相似文献
6.
Petr Hasil 《Journal of Difference Equations and Applications》2017,23(8):1324-1353
We analyse the solution spaces of limit periodic homogeneous linear difference systems, where the coefficient matrices of the considered systems are taken from a commutative group which does not need to be bounded. In particular, we study such systems whose fundamental matrices are not asymptotically almost periodic or which have solutions vanishing at infinity. We identify a simple condition on the matrix group which guarantees that the studied systems form a dense subset in the space of all considered systems. The obtained results improve previously known theorems about non-almost periodic and non-asymptotically almost periodic solutions. Note that the elements of the coefficient matrices are taken from an infinite field with an absolute value and that the corresponding almost periodic case is treated as well. 相似文献
7.
8.
9.
How to avoid order reduction when Lawson methods integrate nonlinear initial boundary value problems
BIT Numerical Mathematics - It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space... 相似文献
10.
The well‐known shallow wave equation can be reduced to the Hirota equation with the aid of corresponding transformation. We discuss its explicit solutions, including dark soliton solution, multiple soliton solution, multiple singular solution, and periodic solutions. 相似文献