We consider the time-dependent one-dimensional nonlinear Schro¨dinger equation with pointwise singular potential. Bymeans of spectral splitting methods we prove that the evolution operator is approximated by the Lie evolution operator,where the kernel of the Lie evolution operator is explicitly written. This result yields a numerical procedure which is muchless computationally expensive than multi-grid methods previously used. Furthermore, we apply the Lie approximation inorder to make some numerical experiments concerning the splitting of a soliton, interaction among solitons and blow-upphenomenon
On the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional l...
International audienceIn this paper, we consider the nonlinear Schrödinger equation ut + iΔu − F(u) ...
Nonlinear evolution equations play enormous significant roles to work with complicated physical phen...
We consider the time-dependent one-dimensional nonlinear Schro\ua8dinger equation with pointwise sin...
In this paper we propose a modified Lie-type spectral splitting approximation where the external po...
Summary. A new method for the numerical simulation of the so-called soliton dynamics arising in a no...
In this work, we consider the numerical solution of the nonlinear Schrödinger equation with a highly...
In this work, we consider the numerical solution of the nonlinear Schrödinger equation with a highly...
International audienceWe consider the linear Schrodinger equation on a one dimensional torus and its...
Abstract. In this paper, we consider the nonlinear Schrödinger equation ut + i∆u − F (u) = 0 in tw...
The computation of the linear Schrödinger equation presents major challenges because of the presenc...
A new method for the numerical simulation of the so-called solitondynamics arising in a nonlinear Sc...
Abstract. We prove an error estimate for a Lie–Trotter splitting operator associated with the Schrö...
AbstractWe introduce a splitting method for the semilinear Schrödinger equation and prove its conver...
The nonlinear Schrödinger equation is a classical field equation that describes weakly nonlinear wav...
On the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional l...
International audienceIn this paper, we consider the nonlinear Schrödinger equation ut + iΔu − F(u) ...
Nonlinear evolution equations play enormous significant roles to work with complicated physical phen...
We consider the time-dependent one-dimensional nonlinear Schro\ua8dinger equation with pointwise sin...
In this paper we propose a modified Lie-type spectral splitting approximation where the external po...
Summary. A new method for the numerical simulation of the so-called soliton dynamics arising in a no...
In this work, we consider the numerical solution of the nonlinear Schrödinger equation with a highly...
In this work, we consider the numerical solution of the nonlinear Schrödinger equation with a highly...
International audienceWe consider the linear Schrodinger equation on a one dimensional torus and its...
Abstract. In this paper, we consider the nonlinear Schrödinger equation ut + i∆u − F (u) = 0 in tw...
The computation of the linear Schrödinger equation presents major challenges because of the presenc...
A new method for the numerical simulation of the so-called solitondynamics arising in a nonlinear Sc...
Abstract. We prove an error estimate for a Lie–Trotter splitting operator associated with the Schrö...
AbstractWe introduce a splitting method for the semilinear Schrödinger equation and prove its conver...
The nonlinear Schrödinger equation is a classical field equation that describes weakly nonlinear wav...
On the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional l...
International audienceIn this paper, we consider the nonlinear Schrödinger equation ut + iΔu − F(u) ...
Nonlinear evolution equations play enormous significant roles to work with complicated physical phen...