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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dean-Kawasaki equation with singular non-local interactions：well-posedness and large deviations
奇异非局部 相互作用 Dean-Kawasaki方程 适定性 大偏差
2023/11/13
The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
High order explicit symplectic integrators for the Discrete Non Linear Schrödinger equation
High order explicit symplectic Discrete Non Linear Schrö dinger equation
2011/3/2
We propose a family of reliable symplectic integrators adapted to the Discrete Non–Linear Schr¨odinger equation; based on an idea of Yoshida [12] we can construct high order numerical schemes, that re...
High order explicit symplectic integrators for the Discrete Non Linear Schrödinger equation
High order explicit symplectic integrators Discrete Non Linear Schrö dinger equation
2010/12/28
We propose a family of reliable symplectic integrators adapted to the Discrete Non–Linear Schr¨odinger equation; based on an idea of Yoshida [12]we can construct high order numerical schemes, that res...
Heteroclinic Orbits for a Discrete Pendulum Equation
heteroclinic solution critical point discrete pendulum equa-tion minimization arguments
2011/2/25
About twenty years ago, Rabinowitz showed firstly that there exist heteroclinic orbits of autonomous Hamiltonian system joining two equilibria. A special case of autonomous Hamiltonian system is the c...
Extinction profile of the logarithmic diffusion equation
logarithmic diffusion equation extinction profile asymptotic behaviour
2011/1/19
Let u be the solution of ut = log u in RN × (0, T ), N ≥ 3, with initial value u0 satisfying Bk1 (x, 0) ≤ u0 ≤ Bk2(x, 0) for some constants k1 > k2 > 0 where Bk(x, t) = 2(N − 2)(T −t)N/(N...
Discrete Nonlinear Schrodinger Equation, Solitons and Organizing Principles for Protein Folding
Discrete Nonlinear Schrodinger Equation Solitons Organizing Principles Protein Folding
2010/12/15
We introduce a novel generalization of the discrete nonlinear Schrodinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35,an arch...
Integrable discretizations for the short wave model of the Camassa-Holm equation
Integrable discretizations short wave Camassa-Holm equation
2010/4/2
The link between the short wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice (2DTL) is clarified. The parametric form of N-cuspon solution of th...
The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral, Goldstone mode, including electroconvection an...
On the dispersionless Kadomtsev-Petviashvili equation in n+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking
Kadomtsev-Petviashvili equation wave breaking n+1 dimensions
2010/4/1
We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi one dimensional wa...
Integrable discretizations of the short pulse equation
Integrable discretizations short pulse equation
2010/4/6
In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms and determinant structure of s...
Asymptotic Behavior for Discretizations of a Semilinear Parabolic Equation with a Nonlinear Boundary Condition
Semidiscretizations Semilinear parabolic equation Asymptotic behavior Convergence
2010/1/22
This paper concerns the study of the numerical approximation for the following initial-boundary value problem: (P) where , and . We show that the solution of a semidiscrete form of (P) goes to ...