Solitary wave solutions to nonlinear evolution equations in mathematical physics

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.     

Measurement of the inclusive charged-current cross section for neutrino and antineutrino scattering on isoscalar nucleons

This paper reports on measurements of the total cross section for the inclusive reaction v_μ+N , as a function of incident energy. Neutrinos and antineutrinos with energy in the range 30–300 GeV were produced in the 1982 Fermilab narrow-band neutrino beamline. A total of 35 000 neutrino and 7000 antineutrino interactions were recorded in the CCFR detector located in LabE. The incident neutrino flux was determined by methods similar to those used in previous experiments. The rate of increase with energy of the total cross section (σ/E _v) in the range 30 to 75 GeV was determined to be 0.659±0.005(stat)±0.039(syst)×10^?38 cm²/GeV and 0.307±0.008(stat)±0.020(syst)×10^?38 cm²/GeV for incident neutrinos and antineutrinos, respectively. The 5.9% systematic errors are due primarily to uncertainties in the flux intensity measurement. The energy dependence of the cross section in the regionE _ν=100–300 GeV was found to be linear, as determined by relative normalization techniques. A weighted average of our previous and present measurement for the total ν-N cross section yields: $$\begin{gathered} \sigma (vN) = 0.666 \pm 0.020(statistical \hfill \\ + systematic)E_v 10^{ - 38} cm^2 ; \hfill \\ \sigma (\bar vN) = 0.324 \pm 0.014(statistical \hfill \\ + systematic)E_v 10^{ - 38} cm^2 ; \hfill \\ \end{gathered} $$ .