arXiv subjects

S. Y. Lou

Publications and source records attributed to S. Y. Lou.

48 records · Page 3Linked to original sources

arXiv2009

Baroclinic equivalent and nonequivalent barotropic modes for rotating stratified flows

In strictly speaking, all the natural phenomena on the earth should be treated under rotating coordinate. The existence of baroclinic nonequivalent barotropic laminar solution for rotating fluids is still open though the laminar solutions for the irrotational fluid had been well studied. In this letter, all the possible equivalent barotropic (EB) laminar solution are firstly explored and all the possible baroclinic non-EB elliptic circulations and hyperbolic laminar modes are discovered. The baroclinic EB circulations (including the vortex streets and hurricane like vortices) possess rich structures because either the arbitrary solutions of arbitrary nonlinear Poison equations can be used or an arbitrary two-dimensional stream function is revealed. The discovery of the baroclinic non-EB modes disproves a known conjecture. The results may be broadly applied in atmospheric and oceanic dynamics, plasma physics, astrophysics and so on.

physics.flu-dyn↗

arXiv2009

Nonsensitive nonlinear homotopy approach

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines perturbation and nonperturbation is constructed. An artificial nonlinear homotopy parameter plays the role of a perturbation parameter, while other artificial nonlinear parameters, of which the original problems are independent, introduced in the nonlinear homotopy models are nonperturbatively determined by means of a principle minimal sensitivity. The method is demonstrated through several quantum anharmonic oscillators and a non-hermitian parity-time symmetric Hamiltonian system. In fact, the framework of the theory is rather general that can be applied to a broad range of natural phenomena. Possible applications to condensed matter physics, matter wave systems, and nonlinear optics are briefly discussed.

physics.comp-ph↗

arXiv2009

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlevé II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.

nlin.PS↗

arXiv2008

Monopole blocking governed by a modified KdV type equation

A type of coupled variable coefficient modified Korteweg-de Vries system is derived from a two-layered fluid system. It is known that the formation, maintenance, and collapse of an atmospheric blocking are always related with large-scale weather or shorts term climate anomalies. One special analytical solution of the obtained system successfully features the evolution cycle of an atmospheric monopole type blocking event. In particular, our theoretical results captures a real monopole type blocking case happened during 19 Feb 2008 to 26 Feb 2008 can be well described by our analytical solution.

physics.ao-ph↗

arXiv2008

Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation

For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlevé II, Painlevé I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutions can be obtained by solving linear ordinary differential equations.

nlin.SI↗

arXiv2008

Evolution of Dipole-Type Blocking Life Cycles: Analytical Diagnoses and Observations

A variable coefficient Korteweg de Vries (VCKdV) system is derived by considering the time-dependent basic flow and boundary conditions from a nonlinear, inviscid, nondissipative, and equivalent barotropic vorticity equation in a beta-plane. One analytical solution obtained from the VCKdV equation can be successfully used to explain the evolution of atmospheric dipole-type blocking (DB) life cycles. Analytical diagnoses show that background mean westerlies have great influence on evolution of DB during its life cycle. A weak westerly is necessary for blocking development and the blocking life period shortens, accompanied with the enhanced westerlies. The shear of the background westerlies also plays an important role in the evolution of blocking. The cyclonic shear is preferable for the development of blocking but when the cyclonic shear increases, the intensity of blocking decreases and the life period of DB becomes shorter. Weak anticyclonic shear below a critical threshold is also favorable for DB formation. Time-dependent background westerly (TDW) in the life cycle of DB has some modulations on the blocking life period and intensity due to the behavior of the mean westerlies. Statistical analysis regarding the climatological features of observed DB is also investigated. The Pacific is a preferred region for DB, especially at high latitudes. These features may associate with the weakest westerlies and the particular westerly shear structure over the northwestern Pacific.

nlin.PS↗

arXiv2008

Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.

nlin.PS↗

arXiv2007

A coupled Volterra system and its exact solutions

A coupled Volterra system is proposed. The model can be considered as one of the integrable discrete form of the coupled integrable KdV system which is a significant physical model. Many types of cnoidal waves, positons, negatons (solitons) and complexitons of the model are obtained by a simple rational expansion method of the Jacobi elliptic functions, trigonometric functions and hyperbolic functions.

nlin.SI↗

arXiv2006

Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlevé property. We then solve the LSRI equation using Painlevé truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.

nlin.SI↗

arXiv2005

Vortices, circumfluence, symmetry groups and Darboux transformations of the Euler equations

The Euler equation (EE) is one of the basic equations in many physical fields such as the fluids, plasmas, condense matters, astrophysics, oceanic and atmospheric dynamics. A new symmetry group theorem of the two dimensional EE is obtained via a simple direct method and the theorem is used to find \em exact analytical \rm vortex and circumfluence solutions. Some types of Darboux transformations (DTs) for the both two and three dimensional EEs are obtained for \em arbitrary spectral parameters \rm which indicates that the EEs are integrable and the Navier-Stockes (NS) equations with large Renoyed number are nearly integrable, i.e, they are singular perturbations of the integrable EEs. The possibility of the vortex and circumfluence solutions to approximately explain the tropical cyclones (TCs), especially, the Hurricane Andrew 1992, is discussed.

nlin.PS↗

arXiv2005

Nonsingular positon and complexiton solutions for the coupled KdV system

Taking the coupled KdV system as a simple example, analytical and nonsingular complexiton solutions are firstly discovered in this letter for integrable systems. Additionally, the analytical and nonsingular positon-negaton interaction solutions are also firstly found for S-integrable model. The new analytical positon, negaton and complexiton solutions of the coupled KdV system are given out both analytically and graphically by means of the iterative Darboux transformations.

nlin.SI↗

arXiv2005

Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlevé test. Three types of $τ$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlevé integrable coupled KdV system there may be multiple soliton solutions.

nlin.SI↗