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The $(N,M)$-bigraded Toda hierarchy is an extension of the original Toda lattice hierarchy. The pair of numbers $(N,M)$ represents the band structure of the Lax matrix which has $N$ upper and $M$ lowe...
Symmetry Groups and Exact Solutions of a (3+1)-dimensional Nonlinear Evolution Equation and Maccari’s System
symmetry group (3+1)-dimensional nonlin ear evolution equation Maccari’s system
2012/9/25
Based on the generalized symmetry group method and symbolic computation, both the Lie point groups and the non-Lie symmetry groups of a (3+1)-dimensional nonlinear evolution equation as well as the Ma...
On rational solutions of multicomponent and matrix KP hierarchies
On rational solutions multicomponent matrix KP hierarchies
2010/11/10
We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discu...
New explicit exact solutions for the Liénard equation and its applications
exact solutions Liénard equation Pochhammer-Chree equation
2010/4/2
In this letter, new exact explicit solutions are obtained for the Li\'enard equation, and the applications of the results to the generalized Pochhammer-Chree equation, the Kundu equation and the gener...
Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
Hodograph solutions scalar function Euler-Poisson-Darboux equation
2010/4/2
It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darbo...
Lie symmetry analysis and exact solutions for a variable coefficient Gardner equation arising in arterial mechanics
Lie symmetry analysis arterial mechanics coefficient Gardner equation
2010/4/2
In this paper, a variable-coefficient Gardner equation is considered. By using the classical symmetry analysis method symmetries for this equation are obtained. Then, the generalized Jacobi elliptic f...
Explicit quasi-periodic wave solutions and asymptotic analysis to the supersymmetric Ito's equation
quasi-periodic wave super-Hirota bilinear asymptotic analysis
2010/4/1
Based on a Riemann theta function and the super-Hirota bilinear form, we propose a key formula for explicitly constructing quasi-periodic wave solutions of the supersymmetric Ito's equation in supersp...
A note on "New abundant solutions for the Burgers equation"
Burgers equation new exact solutions
2010/4/6
Salas, Gomez and Heranandez [A.Y. Salas S., C.A. Gomez S., J.E.C Hernandez, New abundant solutions for tha Burgers equation, Computers and Mathematics with Applications 58 (2009) 514 -520] presented 7...
On some special solutions to periodic Benjamin-Ono equation with discrete Laplacian
Benjamin-Ono equation nonlocal integrable system Macdonald polynomial integrals of motion
2010/4/8
We investigate a periodic version of the Benjamin-Ono (BO) equation associated with a discrete Laplacian. We find some special solutions to this equation, and calculate the values of the first two int...
Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
twisted derivation super KdV equation quasideterminant solutions
2010/4/7
This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twiste...
Positive Solutions for Eigenvalue Problem with Time Scales
time scales positive solution eigenvalues fixed points
2012/9/28
By exploring the values of the eigenvalue ル , this paper deals with the existence and nonexistence of positive solution for the following three-point boundary value problem with time scales: () () (, ...
On some Bounds for the Solutions of the Semi-Discretized Time-Dependent Ginzburg-Landau Equations
Semi-Discretized Time-Dependent Ginzburg-Landau Equations Bounds
2010/3/5
We study the two-dimensional system of Time-Dependent Ginzburg-Landau Equations (TDGL) for modeling a thin film of superconductor subject to a uniform magnetic field. We discretize the TDGL for the sp...