A type of bounded traveling wave solutions for the Fornberg-Whitham equation

In this paper, by using bifurcation method, we successfully find the Fornberg-Whitham equation has a type of traveling wave solutions called kink-like wave solutions and antikinklike wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some concrete data, the graphs of the implicit functions are displayed, and the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.Comment: 14 pages, 10 figure

Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation

We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reasonwhy these solutions can exist in this equation are also given.Comment: 14 pages, 41 figure

Soliton and periodic wave solutions to the osmosis K(2, 2) equation

In this paper, two types of traveling wave solutions to the osmosis K(2, 2) equation are investigated. They are characterized by two parameters. The expresssions for the soliton and periodic wave solutions are obtained.Comment: 14 pages, 16 figure

Effectiveness and chemical pest control of Bt-cotton in the Yangtze River Valley, China

The sustainability of Bt-cotton in China, at least along Yellow River Valley, has been questioned, so this paper examines its effectiveness along Yangtze River Valley, where Bt-cotton is also widely sown, to determine what might be the factors beneath the limited or reduced effectiveness being observed. The analysis is based on the data collected for several years from many locations in the Yangtze River Valley Varietal Experiment Network to provide information on the varieties and their agronomic performance, on the control of their GM characteristic, on the expression of the Bt-gene and on chemical control practices against cotton pests.All varieties declared to be Bt-cotton were confirmed to have the Bt-gene, the expression of which was assessed in three ways: through the analysis of Bt-protein production and through indoor and outdoor bioassays. Gene expression varied substantially between varieties and between years for the few varieties which were tested in two subsequent years.The Bt-cotton varieties being sown cannot control bollworms totally even early in the growing season, so surviving larvae could inevitably be observed, and this led farmers (or professionals in charge of supplying technical assistance to farmers) to spray chemicals regardless of the real infestation level. This demonstrates behaviour aimed at eradication of the pests as bollworms seem to be treated chemically more often than is required and far earlier than necessary on the first two generations of H. armigera. The chemical control of the Bt-cotton in Yangtze River Valley hence is not optimal, thus farmers are paying high prices for varieties which are not totally resistant to bollworms and pest control costs are not reduced to the extent that they might expect, lowering the profitability of cotton production. Also chemical protection costs are not decreasing as those pests unaffected by the Bt-gene, mainly but not exclusively sucking ones are requiring more control. This is illustrative of a phenomenon of pest complex shift which deserves more attention in following up the Bt-cotton use.China; Bt; cotton; gene expression; chemical control; effectiveness