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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solitons and Breathers in the modulus KdV equations
模量 KdV方程 孤子 呼吸器
2023/5/12
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
Local Dynamics Near Unstable Branches of NLS Solitons
Local Dynamics Unstable Branches of NLS Solitons Analysis of PDEs
2012/7/11
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, so...
Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation
Reflection of Channel-Guided Solitons Junctions Two-Dimensional Nonlinear Schroedinger Equation Pattern Formation and Solitons
2012/4/26
Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged....
Inelastic character of solitons of slowly varying gKdV equations
gKdV equations soliton dynamics slowly varying medium
2011/9/21
Abstract: In this paper we describe the inelastic character of solitons of some slowly varying gKdV equations. We give precise lower bounds, in the energy space, of the defect induced by the potential...
A refined empirical stability criterion for nonlinear Schroedinger solitons under spatiotemporal forcing
nonlinear Schroedinger solitons spatiotemporal
2011/7/6
We investigate the dynamics of travelling oscillating solitons of the cubic NLS equation under an external spatiotemporal forcing of the form $f(x,t) = a \exp[iK(t)x]$. For the case of time-independen...
Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective...
Broad Band Solitons in a Periodic and Nonlinear Maxwell System
Periodic Nonlinear Maxwell System nonlocal equations geometrical optics
2011/7/6
We consider the one-dimensional Maxwell equations with low contrast periodic linear refractive index and weak Kerr nonlinearity. In this context, wave packet initial conditions with a single carrier f...
KP solitons and total positivity for the Grassmannian
KP solitons total positivity Grassmannian
2011/7/6
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known th...
KP solitons and total positivity for the Grassmannian
KP solitons total positivity Grassmannian
2011/7/6
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known th...
Scattering of Solitons for Dirac Equation Coupled to a Particle
Scattering of Solitons Dirac Equation Coupled Particle
2011/1/21
We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in...
The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons
Soliton dynamics Nonlinear Schroedinger Equation
2011/2/28
In this paper we present some recent results concerning the existence,the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parameter h → 0.
Effective dynamics for $N$-solitons of the Gross-Pitaevskii equation
Effective dynamics $N$-solitons Gross-Pitaevskii equation
2010/12/13
We consider several solitons moving in a slowly varying external eld. We show that the e ective dynamics obtained by restricting the full Hamiltonian to the nite dimensional manifold of N-solitons (...