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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(I)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(II)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Growth of Sobolev norms in the cubic defocusing nonlinear Schrodinger equation
Sobolev norms cubic defocusing nonlinear Schrodinger equation
2015/9/25
We consider the cubic defocusing nonlinear Schr¨odinger equation in the two dimensional torus. Fix s > 1. Colliander, Keel, Staffilani, Tao and Takaoka proved in [CKS+10] the existence of solutions wi...
Conservativity of Symplectic Methods for the Ablowitz-Ladik Discrete Nonlinear Schrodinger Equation
Nonlinear Schrdinger Equation Ablowitz-Ladik Model Darboux
2012/8/7
Using several kinds of Darboux transformations, we standardize the non-
canonical symplectic structure of Ablowitz-Ladik model (A-L model) of the
Nonlinear Schr膐dinger Equation (NLSE), then we emplo...
Cauchy problem of nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2
Applied mathematics Cauchy problem nonlinear Schrodinger equation local well-posedness scaling limit
2011/10/15
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
On asymptotic stability of moving ground states of the nonlinear Schrodinger equation
asymptotic stability nonlinear Schrodinger equation Analysis of PDEs
2011/9/20
Abstract: We extend to the case of moving solitons, the result on asymptotic stability of ground states of the NLS with a short range linear potential obtained by the author in a previous paper. Now w...
Nonlinear-damping continuation of the nonlinear Schrodinger equation - a numerical study
Nonlinear-damping continuation nonlinear Schrodinger equation Analysis of PDEs
2011/9/13
Abstract: We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in ...
Stationary Nonlinear Schrodinger Equation on Simplest Graphs: Boundary conditions and exact solutions
Nonlinear Schrodinger Equation Simplest Graphs Mathematical Physics
2011/9/29
Abstract: We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs co...
Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
periodic waves solitons the nonlinear Schrodinger equation
2010/11/18
Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a w...
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...
Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients
Inhomogeneous NLS equation with variable coefficients Similarity transformation
2010/12/16
The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr¨odinger equation with variable coefficients in terms of rational-like functions by using the similarity transforma...
Travelling wave solutions to nonlinear Schrodinger equation with self-steepening and self-frequency shift
group velocity dispersion nonlinear Schrodinger equation self-frequency shift
2010/4/7
We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion. We show that this system possesses a rich solution space with a ...
Canonical reduction of the self-dual Yang-Mills equations to inhomogeneous nonlinear Schrodinger equation and exact solutions
Nonlinear evolution equations Yang-Mills theory
2010/9/14
The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional inhomogeneous nonlinear Schr¨odinger equation are considered. On the other hand, other methods ...
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...
In this paper we consider the following nonlinear Schr\"{o}dinger equation: iu_t+Δu+|u|~2u=0 in R~3×R_+,u(0)=u_0∈H~2(R~3). First we give a sufficient condition on the initial data which guarantees the...