Zuntao Fu

JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS

Abstract A Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method, is proposed to construct the exact periodic solutions of nonlinear wave equations. It is shown that the periodic solutions obtained by this method include some shock wave solutions and solitary wave solutions.

New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations

Abstract New Jacobi elliptic functions are applied in Jacobi elliptic function expansion method to construct the exact periodic solutions of nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this method and more shock wave solutions or solitary wave solutions can be got at their limit condition.

New transformations and new approach to find exact solutions to nonlinear equations

New transformations from the nonlinear sine-Gordon equation are shown in this Letter, based on them a new approach is proposed to construct exact periodic solutions to nonlinear equations. It is shown that more new periodic solutions can be obtained by this new approach and more shock wave solutions or solitary wave solutions can be got under their limit condition.

New kinds of solutions to Gardner equation

Abstract On the basis of analysis to the projective Riccati equations, an intermediate transformation in expansion method is constructed. And this transformation is applied to solve Gardner equation, there many new kinds of travelling wave solutions including solitary wave solution are obtained, in which some are found for the first time.

Detrended Partial-Cross-Correlation Analysis: A New Method for Analyzing Correlations in Complex System

In this paper, a new method, detrended partial-cross-correlation analysis (DPCCA), is proposed. Based on detrended cross-correlation analysis (DCCA), this method is improved by including partial-correlation technique, which can be applied to quantify the relations of two non-stationary signals (with influences of other signals removed) on different time scales. We illustrate the advantages of this method by performing two numerical tests. Test I shows the advantages of DPCCA in handling non-stationary signals, while Test II reveals the “intrinsic” relations between two considered time series with potential influences of other unconsidered signals removed. To further show the utility of DPCCA in natural complex systems, we provide new evidence on the winter-time Pacific Decadal Oscillation (PDO) and the winter-time Nino3 Sea Surface Temperature Anomaly (Nino3-SSTA) affecting the Summer Rainfall over the middle-lower reaches of the Yangtze River (SRYR). By applying DPCCA, better significant correlations between SRYR and Nino3-SSTA on time scales of 6 ~ 8 years are found over the period 1951 ~ 2012, while significant correlations between SRYR and PDO on time scales of 35 years arise. With these physically explainable results, we have confidence that DPCCA is an useful method in addressing complex systems.

The JEFE method and periodic solutions of two kinds of nonlinear wave equations

Abstract The Jacobi elliptic function expansion (JEFE) method is applied to construct the exact periodic solutions to two kinds of nonlinear wave equations, such as BBM equation, fifth-order dispersive equation, Kawahara equation, modified Kawahara equation, second-order BO equation and symmetrical-regular long wave equation. The corresponding shock wave solutions or solitary wave solutions are obtained as special cases of the periodic solutions. It is shown that this method is very powerful for some nonlinear wave equations, and its applying domain is given.

Exact Solutions to Double and Triple Sinh-Gordon Equations

In this paper, two transformations are introduced to solve double sinh-Gordon equation and triple sinh-Gordon equation, respectively. It is shown that different transformations are required in order to obtain more kinds of solutions to different types of sinh-Gordon equations. - PACS: 03.65.Ge

Extracting climate memory using Fractional Integrated Statistical Model: A new perspective on climate prediction

Long term memory (LTM) in climate variability is studied by means of fractional integral techniques. By using a recently developed model, Fractional Integral Statistical Model (FISM), we in this report proposed a new method, with which one can estimate the long-lasting influences of historical climate states on the present time quantitatively, and further extract the influence as climate memory signals. To show the usability of this method, two examples, the Northern Hemisphere monthly Temperature Anomalies (NHTA) and the Pacific Decadal Oscillation index (PDO), are analyzed in this study. We find the climate memory signals indeed can be extracted and the whole variations can be further decomposed into two parts: the cumulative climate memory (CCM) and the weather-scale excitation (WSE). The stronger LTM is, the larger proportion the climate memory signals will account for in the whole variations. With the climate memory signals extracted, one can at least determine on what basis the considered time series will continue to change. Therefore, this report provides a new perspective on climate prediction.

Beyond Benford's Law: Distinguishing Noise from Chaos.

Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benfords law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly.

Different multi-fractal behaviors of diurnal temperature range over the north and the south of China

Multi-fractal behaviors of diurnal temperature range (DTR for short) from 100 stations over China during 1956–2010 are analyzed by means of multi-fractal detrended fluctuation analysis. By making a Monte-Carlo simulation, we obtain two criterions which can be used to decide whether a DTR series is significantly multi-fractal or not. With these criterions, different multi-fractal behaviors are found over the north and the south of China, and Yangtze River is roughly the dividing line. Over the north region, nearly all the considered DTR series do not show multi-fractal behaviors, while the results are completely the opposite over the south. The findings are confirmed by the scaling behaviors of the corresponding DTR magnitude series and indicate that more scale-dependent structure differences may be hidden in DTR series over the north and the south of China. Therefore, an extensive analysis of the multi-fractal behaviors are essential for a better understanding of the complex structures of the climate changes.