相关论文: Painlev\'{e} Analysis and Exact Solutions of a Mod…
After a brief introduction to the Painlev\'{e} property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painlev\'{e} tests. The tests are…
An alternate form of discrete potential Boussinesq equation is proposed and its multisoliton solutions are constructed. An ultradiscrete potential Boussinesq equation is also obtained from the discrete potential Boussinesq equation using…
The ``Painlev\'e analysis'' is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject which is in fact the theory…
This short survey presents the essential features of what is called Painlev\'e analysis, i.e. the set of methods based on the singularities of differential equations in order to perform their explicit integration. Full details can be found…
Starting from the second Painlev\'{e} equation, we obtain Painlev\'{e} type equations of higher order by using the singular point analysis.
This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether…
In this work the longitudinal wave equation through magneto-electro-elastic circular rod is studied analytically. Painlev\'e test is performed to check integrability of the equation. Exact solitary wave solutions are found by homogeneous…
The Painlev\'e test is a widely applied and quite successful technique to investigate the integrability of nonlinear ODEs and PDEs by analyzing the singularity structure of the solutions. The test is named after the French mathematician…
Based the homogeneous balance method, a general method is suggested to obtain several kinds of exact solutions for some kinds of nonlinear equations. The validity and reliability of the method are tested by applying it to the Bousseneq…
A direct method for calculation of Miura type transformations via LA pair is used for the Boussinesq equation. Quadratic Miura type transformations connected with local weakly-nonlocal (Maltsev-Novikov) Hamiltonian structures. Modified…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
The Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics. We show the existence of continuous periodic weak solutions of the Boussinesq equations which satisfies the…
A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.
The Painlev\'e analysis introduced by Weiss, Tabor and Carnevale (WTC) in 1983 for nonlinear partial differential equations (PDE's) is an extension of the method initiated by Painlev\'e and Gambier at the beginning of this century for the…
Using the Painlev\'e--Kovalevskaya test, we find several new matrix generalizations of the Painlev\'e-4 equation. Some limiting transitions reduce them to known matrix Painlev\'e-2 equations.
This work investigates the long-time asymptotic behaviors of initial value problem for the good Boussinesq equation and the modified Boussinesq equation in Painlev\'{e} region. The Deift-Zhou steepest descent method is used to deform the…
In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…
The $q$-Painlev\'e equation of type $E^{(1)}_6$ is obtained by Pad\'e method. Special solutions in determinant formula to the $q$-Painlev\'e equation is presented. A relation between Pad\'e method and B\"acklund transformation of type…
We examine by singularity analysis an equation derived by reduction using Lie point symmetries from the Euler--Bernoulli Beam equation which is the Painlev\'{e}--Ince Equation with additional terms. The equation possesses the same…
Necessary discretization rules to preserve the Painlev\'e property are stated. A new method is added to the discrete Painlev\'e test, which perturbs the continuous limit and generates infinitely many no-log conditions.