arXiv subjects

Sen-Yue Lou

Publications and source records attributed to Sen-Yue Lou.

8 recordsLinked to original sources

arXiv2022

High precision solutions to quantized vortices within Gross-Pitaevskii equation

The dynamics of vortices in Bose-Einstein condensates of dilute cold atoms can be well formulated by Gross-Pitaevskii equation. To better understand the properties of vortices, a systematic method to solve the nonlinear differential equation for the vortex to a very high precision is proposed. Through two-point Pad$\acute{\text{e}}$ approximants, these solutions are presented in terms of simple rational functions, which can be used in the simulation of vortex dynamics. The precision of the solutions is sensitive to the connecting parameter and the truncation orders. It can be improved significantly with a reasonable extension in the order of rational functions. The errors of the solutions and the limitation of two-point Pad$\acute{\text{e}}$ approximants are discussed. This investigation may shed light on the exact solution to the nonlinear vortex equation.

nlin.PS↗

arXiv2017

From nothing to something II: nonlinear systems via consistent correlated bang

Chinese ancient sage Laozi said everything comes from \emph{\bf \em "nothing"}. \rm In the first letter (Chin. Phys. Lett. 30 (2013) 080202), infinitely many discrete integrable systems have been obtained from "nothing" via simple principles (Dao). In this second letter, a new idea, the consistent correlated bang, is introduced to obtain nonlinear dynamic systems including some integrable ones such as the continuous nonlinear Schrödinger equation (NLS), the (potential) Korteweg de Vries (KdV) equation, the (potential) Kadomtsev-Petviashvili (KP) equation and the sine-Gordon (sG) equation. These nonlinear systems are derived from nothing via suitable "Dao", the shifted parity, the charge conjugate, the delayed time reversal, the shifted exchange, the shifted-parity-rotation and so on.

nlin.SI↗

arXiv2015

Primary branch solutions of first order autonomous scalar partial differential equations

A primary branch solution (PBS) is defined as a solution with $n$ independent $m-1$ dimensional arbitrary functions for an $n$ order $m$ dimensional partial differential equation (PDE). PBSs of arbitrary first order scalar PDEs can be determined by using Lie symmetry group approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary (1+1)-dimensional first order autonomous PDEs. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be find by fixing the arbitrary functions and selecting different seed solutions.

math-ph↗

arXiv2014

Nonlocal conservation laws and related Bäcklund transformations via reciprocal transformations

A set of infinitely many nonlocal conservation laws are revealed for (1+1)-dimensional evolution equations. For some special known integrable systems, say, the KdV and Dym equations, it is found that different nonlocal conservation laws can lead to same new integrable systems via reciprocal transformation. On the other hand, it can be considered as one solution of the new model obtained via reciprocal transformation(s) can be changed to different solutions of the original model. The fact indicates also that two or more different (local and nonlocal) conservation laws can be used to find implicit auto-Bäcklund transformations via reciprocal transformation to other systems.

nlin.SI↗

arXiv2013

A new optical field state as an output of diffusion channel when the input being number state

We theoretically propose a new optical field state which is named Laguerre-polynomial-weighted chaotic field. We show that such state can be implemented, i.e., when a number state enters into a diffusion channel, the output state is just this kind of states. We solve the master equation describing the diffusion process by using the summation method within ordered product of operators and the entangled state representaion. The solution manifestly shows how a pure state evolves into a mixed state. The physical difference between the diffusion and the amplitude damping is pointed out.

physics.optics↗

arXiv2013

Damping law of photocount distribution in a dissipative channel

For a dissipative channel governed by the master equation of density operator}$dρ/dt=κ\left(2aρa^{\dagger}-a^{\dagger}aρ-ρa^{\dagger}a\right) ,${\small \ we find that photocount distribution formula at time}$t,${\small \}$p\left(n,t\right) =Tr\left\{ρ\left(t\right) \mathbf{\colon}\left(ξa^{\dagger}a\right) ^{n}e^{-ξa^{\dagger}a}/n!\colon \right\} ,${\small \ becomes}$p\left(n,t\right) =Tr% \left[ ρ\left(0\right) \mathbf{\colon}\left(ξe^{-2κt}a^{\dagger}a\right) ^{n}e^{-ξe^{-2κt}a^{\dagger}a}/n!\colon % \right] ,${\small \ as if the quantum efficiency}$ξ${\small \ of the detector becomes}$ξe^{-2κt}${\ This law greatly simplifies the theoretical study of photocount distribution for quantum optical field.

quant-ph↗

arXiv2012

Interactions among different types of nonlinear waves described by the Kadomtsev-Petviashvili Equation

In nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlevé waves. In this paper, the nonlocal symmetries related to the Darboux transformations (DT) of the Kadomtsev-Petviashvili (KP) equation is localized after imbedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant solutions such that interaction solutions among different types of nonlinear waves can be found. It is shown that starting from a Boussinesq wave or a KdV-type wave, which are two basic reductions of the KP equation, the essential and unique role of the DT is to add an additional soliton.

nlin.SI↗

arXiv2008

Nonlocal symmetries for bilinear equations and their applications

In this paper, nonlocal symmetries for the bilinear KP and bilinear BKP equations are re-studied. Two arbitrary parameters are introduced in these nonlocal symmetries by considering gauge invariance of the bilinear KP and bilinear BKP equations under the transformation $f\longrightarrow fe^{ax+by+ct}$. By expanding these nonlocal symmetries in powers of each of two parameters, we have derived two types of bilinear NKP hierarchies and two types of bilinear NBKP hierarchies. An impressive observation is that bilinear positive and negative KP and BKP hierarchies may be derived from the same nonlocal symmetries for the KP and BKP equations. Besides, as two concrete examples, we have deived bilinear Bäcklund transformations for $t_{-2}$-flow of the NKP hierarchy and $t_{-1}$-flow of the NBKP hierarchy. All these results have made it clear that more nice integrable properties would be found for these obtained NKP hierarchies and NBKP hierarchies. Since KP and BKP hierarchies have played an essential role in soliton theory, we believe that the bilinear NKP and NBKP hierarchies will have their right place in this field.

nlin.SI↗