Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rational, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating the dynamics of the obtained solutions. The results of the present paper help to reveal the existence of rational wave structures of different types for the 2D-HB equation

Mapping of Soil Saturated Hydraulic Conductivity in Navroud-Assalem Watershed in Guilan Province

Introduction: With increasing awareness of human beings towards the environment, researchers pay more attention to process and redistribution of water flow and solute transport in the soil and groundwater. Moreover, determination of soil hydraulic conductivity is necessary to determine the runoff from basins. Water movement within the unsaturated zone is often described by the formulae proposed by Richards. To solve this equation, initial and boundary conditions of the hydraulic conductivity and the soil water pressure should be determined as functions of soil water content. Beerkan method was developed to identify retention and hydraulic conductivity curves. In this method, van Gunechten with Burdine condition and Brooks and Corey equations were used to describe water retention and hydraulic conductivity curves. Recognition of the spatial pattern of studied parameter using semivariogram and then preparing zoning map with interpolation methods such as IDW and kriging can help us in relevant watershed management. The aim of this study was to spatial analyze of saturated hydraulic conductivity from 50 infiltration tests at watershed scale using Beerkan method and then preparing zoning map for the Navroud watershed. Materials and Methods: Navroud-Assalem watershed with an area of about 307 km2 is located in the west part of Guilan province, within the city of Talesh. Of the total watershed area of Navroud, about 41 km2 is plains and the rest of it is about 266 km2, corresponding to the mountainous area. The study area includes an area with a height above 130 m. In order to complete the database of the studied watershed the present study was designed to assess soil saturated hydraulic conductivity. In this study, a 2×2 km network was designed in Navroud watershed with a surface area of 307 km2, and then infiltration tests were carried out in each node using single ring of Beerkan. Beerkan method derives shape parameters from particle-size distribution and normalization parameters from infiltration test with a near zero pressure head. Evaluation of spatial variation was done using GS+ and zoning map was prepared with ArcGIS software. Statistical evaluation of recorded data was done using SPSS software package. Results and Discussion: Results showed that the soil bulk density was of 1.07 gr cm-3 in average. Furthermore, the results showed that the average of saturated hydraulic conductivity (Ks) in the watershed was of 3.96 cm hr-1 with a coefficient of variation of 151%. The watershed Ks is classified in the moderate class. Regarding the high value of Ks variation coefficient, using geostatistics is necessary to analyze Ks spatial variation. The results indicate the absence of the anisotropy. Using GS+ software, exponential model was fit on the empirical variation (r2=0.953 and RSS=0.0057 cm hr-1). The effective range was of 2280 m. The difference between the amounts reported by other studies and this study was because of the effect of the difference in the study area (307 km, in this study), scale (the field or watershed) and the distance between measured points. Two usual methods of interpolation including inverse distance weighting and ordinal kriging were verified. The results showed that ordinal kriging performed better than inverse distance weighting method (RMSEs for ordinal kriging and inverse distance weighting were 8.97 and 9.75, respectively). Zoning map of Ks was prepared according to the results of GS+ software using ArcGIS software. The correlation coefficients between Ks and sand, silt and clay percents were -0.04, 0.01 and 0.07, which demonstrate a weak effect of soil texture on the Ks as compared with soil structure. The correlation coefficient of the soil bulk density with Ks was of -0.45 which demonstrate a stronger effect as compared with the soil texture. Conclusions: The results of this study can be used to proper management of watersheds. One of the main information needed to manage a watershed is Ks. Determining the spatial variability of soil saturated hydraulic conductivity at watershed scale in spite of its difficulty is one of the main prerequisite parameters to provide detailed maps of a watershed. The aim of this study was to analyze the spatial variability of Ks in Navroud-Assalem watershed, Guilan province. After analyzing spatial data, using ordinary kriging interpolation method, zoning map of Ks was prepared. This map can be used to find the optimal management of watershed, such as determining the amount of basin runoff and groundwater recharge