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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On a generalized Sasa-Satsuma equation (II)
广义 萨萨-萨摩方程 达尔布变换 孤子解 Darboux变换
2023/5/8
In this talk, we will investigate the Darboux transformation and soliton solutions for a generalized Sasa-Satsuma (gSS) equation. We first give the construction of Darboux transformation, and then we ...
SWEEPING PRECONDITIONER FOR THE HELMHOLTZ EQUATION: MOVING PERFECTLY MATCHED LAYERS
Helmholtz equation perfectly matched layers high frequency waves preconditioners LDLt factorization Green’s function multifrontal methods optimal ordering
2015/7/14
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure o...
Asymptotics of the Solutions of the Random Schrödinger Equation
Asymptotics of the Solutions Random Schrö dinger Equation
2015/7/14
We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then ...
Extremal Functions for a Mean Field Equation in Two Dimension
Extremal Functions a Mean Field Equation Two Dimension
2014/4/3
Let be a bounded piecewise C 2 simply-connected domain. In thisarticle, we give necessary and sucient conditions for the existence ofmaximizer ofJ8( ) = log Zedx!116Zj 5 j2dx for 2 H10(). We pro...
Characteristic Set Algorithms for Equation Solving in Finite Fields and Applications in Cryptanalysis
Characteristic set finite field proper triangular set regular triangular set Boolean function stream cipher
2013/9/9
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula ...
Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
the first Painlevé hierarchy non-generic critical behavior the KdV equation
2011/8/23
Abstract: We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the d...
On combinatorial invariance of the cohomology of Milnor fiber of arrangements and Catalan equation over function field
Milnor fiber arrangements Catalan equation function field
2010/11/8
We show that for arrangements of lines with points of multiplicity at most three, the cohomology of Milnor fiber is determined only by the combinatorics of arrangement. The proof depends on enumeratio...
Gradient estimates for a simple nonlinear heat equation on manifolds
nonlinear heat equation gradient estimate
2010/11/29
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem ut − u = au log u + V u, u > 0 on the compact Riemannian manifold (M, g) of...
Stability of a Generalized Mixed Type Additive, Quadratic, Cubic and Quartic Functional Equation
Additive function Quadratic function Cubic function Quartic function Generalized Hyers-Ulam-Rassias stability Ulam-Gavruta-Rassias stability J.M. Rassias stability
2010/4/16
In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the generalized mixed type of functional equation for fixed integers with ![]()
EIGHT=...
Approximation of a Mixed Functional Equation in Quasi-Banach Spaces
Generalized Hyers-Ulam stability additive function cubic function quasi-Banach space $p$-Banach space
2010/1/22
In this paper we establish the general solution of the functional equation and investigate its generalized Hyers-Ulam stability in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stab...
Existence of a Continuous Solution of Parametric Nonlinear Equation with Constraints
Continuous Solution Parametric Nonlinear Equation Constraints
2009/1/16
Combining a consequence of the Michael continuous selection theorem and an iterative scheme we prove the existence of a continuous solution of a parametric equation with constraints. An inverse functi...
NOTE ON THE DIOPHANTINE EQUATION
2007/12/13
<正> Dr.Erd(?)s conjectured that the Diophantine equation(1)x~x y~y=z~zhas no integer solution, if,x>1,y>1.z>1.In the present note,Ⅰshall prove that his conjecture is correct ouly (?)(x,y)=1 and(1)has ...
Poisson Equation on Some Complete Noncompact Manifolds
Poisson equation heat equation Green's function
2007/12/11
We study the Poisson equation on some complete noncompact manifolds with asymptotically nonnegative curvature. We will also study the limiting behavior of the nonhomogeneous heat equation on some comp...
Pseudo almost periodic solutions of a singularly perturbed differential equation with piecewise constant argument
Singular perturbation Pseudo-almost periodic solutions Pseudo-almost periodic sequences Piecewise constant argument
2007/12/11
Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In a...
A Numerical Solution of Wave Equation Arising in Non-Homogeneous Cylindrical Shells
Hyperbolic equation Difference schemes Stability
2010/2/25
A numerical solution of wave equation arising in non-homogeneous cylindrical shells\ is considered. Stable numerical schemes are developed. The stability estimates for the solution of these difference...