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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...
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...
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...
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 (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...
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 ...
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...
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...
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...
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 ...
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...
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...
2005Vol.43No.6pp.961-964DOI: Exact Solutions for a Nonisospectral and Variable-Coefficient KdV Equation DENG Shu-Fang Institute of Mathematics, Fudan University, Shangha...
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...

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