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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient
VC-PINN 变系数 偏微分方程 正逆问题 变系数物理 知情神经网络
2023/11/13
The talk proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations-Variable Coefficient Physics-Informed Neural N...
CK Method And Auto-Backlund Transformation To Find New Exact Solutions Of The (1+1)-Dimensional Variable-Coefficient KdV Equation
CK Method auto-B¨acklund transformation soliton-type solutions
2011/10/18
In this letter, based on the computerized symbolic computation, we extend the Clarkson and Kruskal (CK) method to search for new soliton-type solutions and auto-B¨acklund transformation of partial dif...
Adomian decomposition method (ADM) for nonlinear wave-like equations with variable coefficient
Adomian decomposition wave-like equation variable coefficient
2010/9/27
The Adomian Decomposition Method (ADM) has been widely applied in solving partial differential equations which represent various phenomena in engineering and physics. This method is easy to program an...
L^3 estimates for an algebraic variable coefficient Wolff circular maximal function
L^3 estimates algebraic variable coefficient Wolff circular maximal function
2011/1/17
In 1997, Thomas Wol proved sharp L3 bounds for his circular maximal function, and in 1999, Kolasa and Wol proved certain non-sharp Lp inequalities for a broader class of maximal functions arising fr...
Reduction operators of variable coefficient semilinear diffusion equations with an exponential source
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
2010/11/10
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ ar...
On integrability of variable coefficient nonlinear Schrodinger equations
variable coefficient nonlinear Schrodinger Lax pairs technique group-theoretical
2010/4/21
We apply Painlev\'e test to the most general variable coefficient nonlinear Schrodinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by ...
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...
Tanh-travelling wave solutions and reduction of variable-coefficient unstable nonlinear Schrodinger equation to a quadrature in electron beam plasma
variable -coefficient unstable nonlinear Schrö dinger (vcUNLS) equation travelling wave solutions, RQ method
2010/9/14
The unstable system of plasma equations where an electron beam is injected under a high-frequency electric field is reduced to the variable -coefficient unstable nonlinear Schrödinger (vcUNLS) eq...
An alternative exact solution method for the reduced wave equation with a variable coefficient
Helmholtz equation Differential equation
2010/9/16
In this paper we present the exact solution of reduced wave equation with a variable coefficient Δu(x) + k2n(x)u(x) = 0 for n(x) = n(r) ,r = |x| by the solution of a classic Riccati differential equat...
ON THE BOUNDARY STABILIZATION OF WAVE EQUATION WITH VARIABLE COEFFICIENT
Wave equation boundary feedback expone
2007/12/10
摘要 This paper is concerned with the stabilization problem of wave equation with variable coefficient under boundary feedback control. It is shown that the energy of the system decays exponentially if ...
General Symmetry Approach to
Solve Variable-Coefficient Nonlinear Equations
symmetry approach variable coefficient equation
2007/8/15
2001Vol.35No.6pp.641-646DOI:
General Symmetry Approach to
Solve Variable-Coefficient Nonlinear Equations
RUAN Hang-Yu,1,2 CHEN Yi-Xin2 and LOU Sen-Yue1
1 Institute of Mo...
Variable-Coefficient Mapping Method Based on Elliptical Equation
and Exact Solutions to Nonlinear Schrödinger Equations with
Variable Coefficient
variable-coefficient mapping method based on elliptical equation nonlinear Schrö dinger equation Jacobian elliptic function
solutions solitonic solutions trigonometric function solutions
2007/8/15
2006Vol.46No.4pp.656-662DOI:
Variable-Coefficient Mapping Method Based on Elliptical Equation
and Exact Solutions to Nonlinear Schrödinger Equations with
Variable Coefficient
...
A Generalized Variable-Coefficient Algebraic Method Exactly
Solving (3+1)-Dimensional Kadomtsev-Petviashvilli Equation
generalized variable-coefficient algebraic method
(3+1)-dimensional KP equation exact explicit solutions
2007/8/15
2005Vol.44No.5pp.821-826DOI:
A Generalized Variable-Coefficient Algebraic Method Exactly
Solving (3+1)-Dimensional Kadomtsev-Petviashvilli Equation
BAI Cheng-Lin,1 BAI Cheng-Jie,2...
Exact Solutions for a Nonisospectral and Variable-Coefficient KdV Equation
nonisospectral and variable-coefficient KdV equation Hirota
method Wronskian technique transformation
2007/8/15
2005Vol.43No.6pp.961-964DOI:
Exact Solutions for a Nonisospectral and Variable-Coefficient KdV Equation
DENG Shu-Fang
Institute of Mathematics, Fudan University, Shangha...
Symmetry Reductions of Two-Dimensional Variable Coefficient
Burgers Equation
variable coefficient Burgers equation symmetry reduction
2007/8/15
2005Vol.43No.5pp.861-866DOI:
Symmetry Reductions of Two-Dimensional Variable Coefficient
Burgers Equation
ZHANG Xiao-Ling1 and LI Biao1,2
1 Department of Applied Mathema...