Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.

Time-delayed bilateral teleoperation using wave variable with prediction in three channel control architecture

This paper proposes a novel method for incorporating wave domain prediction in a three-channel(3CH)architecture,which is the optimal architecture from a transparency point of view,to overcome the poor transparency problem of using the wave variable method in a time-delay teleoperation system.A 3CH teleoperation control architecture is established by selecting parameters of the 4CH architecture sensibly for the system without force sensor in the master side.The communication channel is divided into a two-port model by combining force and velocity information reasonably to extend the wave variable method to a 3CH architecture.Then the I/O signal of the two-port model is transformed into wave variable.A predictor is added to the wave domain of the master side to further improve the transparency of the system,and a regulator is designed to ensure the passivity of the predictor.Experimental results show that the proposed method can guarantee stability and improve the transparency of the teleoperation system with time-delay.

A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation

In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is established.Secondly,the differential matrix is used to simplify the given differential equations on a given test node.Finally,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers problems.In addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.

Bilateral teleoperation with reducing wave-based reflections

This paper presents a wave-based bilateral teleoperation structure to reduce the wave reflection and enhance the force and speed tracking performance through adjusting the relative parameters. A time domain passive approach is also applied to deal with the passivity of whole system even with non passive environment. The efficiency of the proposed method is confirmed by some experimental results.

Global existence of solutions of the critical semilinear wave equations with variable coefficients outside obstacles

In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence.

Weighted L^2-Estimates of Solutions for Damped Wave Equations with Variable Coefficients

The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).

Evolution of the 2015/16 El Nio and historical perspective since 1979

The 2015/16 El Nio developed from weak warm conditions in late 2014 and NINO3.4 reached 3℃ in November 2015. We describe the characteristics of the evolution of the 2015/16 El Nio using various data sets including SST, surface winds,outgoing longwave radiation and subsurface temperature from an ensemble operational ocean reanalyses, and place this event in the context of historical ENSO events since 1979. One salient feature about the 2015/16 El Nio was a large number of westerly wind bursts and downwelling oceanic Kelvin waves(DWKVs). Four DWKVs were observed in April-November 2015 that initiated and enhanced the eastern-central Pacific warming. Eastward zonal current anomalies associated with DWKVs advected the warm pool water eastward in spring/summer. An upwelling Kelvin wave(UWKV) emerged in early November 2015 leading to a rapid decline of the event. Another outstanding feature was that NINO4 reached a historical high(1.7℃), which was 1℃(0.8℃) higher than that of the 1982/83(1997/98) El Nio . Although NINO3 was comparable to that of the 1982/83 and 1997/98 El Nio , NINO1+2 was much weaker. Consistently, enhanced convection was displaced 20 degree westward, and the maximum D20 anomaly was about 1/3.1/2 of that in 1997 and 1982 near the west coast of South America.

Multi-scale variability of the tropical Indian Ocean circulation system revealed by recent observations

The tropical Indian Ocean circulation system includes the equatorial and near-equatorial circulations, the marginal sea circulation, and eddies. The dynamic processes of these circulation systems show significant multi-scale variability associated with the Indian Monsoon and the Indian Ocean dipole. This paper summarizes the research progress over recent years on the tropical Indian Ocean circulation system based on the large-scale hydrological observations and numerical simulations by the South China Sea Institute of Oceanology(SCSIO), Chinese Academy of Sciences. Results show that:(1) the wind-driven Kelvin and Rossby waves and eastern boundary-reflected Rossby waves regulate the formation and evolution of the Equatorial Undercurrent and the Equatorial Intermediate Current;(2) the equatorial wind-driven dynamics are the main factor controlling the inter-annual variability of the thermocline in the eastern Indian Ocean upwelling;(3) the equatorial waves transport large amounts of energy into the Bay of Bengal in forms of coastal Kelvin and reflected free Rossby waves. Several unresolved issues within the tropical Indian Ocean are discussed:(i) the potential effects of the momentum balance and the basin resonance on the variability of the equatorial circulation system, and(ii) the potential contribution of wind-driven dynamics to the life cycle of the eastern Indian Ocean upwelling. This paper also briefly introduces the international Indian Ocean investigation project of the SCSIO, which will advance the study of the multi-scale variability of the tropical Indian Ocean circulation system, and provide a theoretical and data basis to support marine environmental security for the countries around the Maritime Silk Road.

Assorted soliton structures of solutions for fractional nonlinear Schrodinger types evolution equations

Fractional order nonlinear evolution equations have emerged in recent times as being very important model for depicting the interior behavior of nonlinear phenomena that exist in the real world.In particular,Schrodinger-type fractional nonlinear evolution equations constitute an aspect of the field of quantum mechanics.In this study,the(2+1)-dimensional time-fractional nonlinear Schrodinger equation and(1+1)-dimensional time-space fractional nonlinear Schrodinger equation are revealed as having different and novel wave structures.This is shown by constructing appropriate analytic wave solutions.A success-ful implementation of the advised rational(1/φ'(ξ))-expansion method generates new outcomes of the considered equations,by comparing them with those already noted in the literature.On the basis of the conformable fractional derivative,a composite wave variable conversion has been used to adapt the suggested equations into the differential equations with a single independent variable before applying the scheme.Finally,the well-furnished outcomes are plotted in different 3D and 2D profiles for the purpose of illustrating various physical characteristics of wave structures.The employed technique is competent,productive and concise enough,making it feasible for future studies.

Interannual modulation of intraseasonal sea level variability along the southern coast of Java

The intraseasonal variability(ISV) of sea level anomalies(SLAs) along the southern coast of Java and its interannual modulation were studied based on a gridded SLA product produced from the Archiving, Validation, and Interpretation of Satellite Oceanography dataset. This ISV is induced by the propagation of intraseasonal Kelvin waves derived from the central equatorial Indian Ocean(EIO). Wavelet analysis and empirical mode decomposition of intraseasonal SLAs along the southern coast of Java showed interannual variability, with weaker ISV events during El Ni years and positive Indian Ocean Dipole(IOD) years than during normal years. This interannual modulation of the ISV is influenced by the El Ni-Southern Oscillation teleconnection via the Walker Circulation and eastern Indian Ocean upwelling connected to IOD events. The anomalously weaker Walker Circulation during El Ni events generates anomalous surface easterlies over the central-eastern tropical Indian Ocean that produce upwelling Kelvin waves in the EIO and offshore water transport along the southern coasts of Sumatra and Java, resulting in negative SLAs along the southern coast of Java. These negative SLAs damp the positive SLAs induced by the eastward propagation of downwelling Kelvin waves from the central EIO during the following March–May of El Ni years. Similar features of SLAs and sea surface wind anomalies also occur during positive IOD years. Consequently, the sea level ISV along the southern coast of Java is weaker in El Ni and positive IOD years.