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The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one describes reproduction with different phenotypes. Linear stability analysis of the homogeneous in space stationary solution is carried out. Existence of travelling waves is proved in the case of narrow kernels of the integrals. Periodic travelling waves are observed in numerical simulations. Existence of stationary solutions in the form of pulses is shown, and transition from periodic waves to pulses is studied. In the applications to the speciation theory, the results of this work signify that new species can emerge only if they do not have common offsprings. Thus, it is shown how Darwin's definition of species as groups of morphologically similar individuals is related to Mayr's definition as groups of individuals that can breed only among themselves., Comment: 15 pages, 4 figures

An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau -Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU) problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries (mKdV) equation. This model has application from laboratory to astrophysical plasmas as well as biological systems., Comment: 5 pages, 2 figures

Recently we showed that while the tensor force plays an important role in nuclear matter saturation in non-relativistic studies, it does not do so in relativistic studies. The reason behind this is the role of $M^*$, the sum of nucleon mass and its attractive self-energy in nuclear matter. Yet nonrelativistic calculations at a certain level of approximation are far less difficult than comparative relativistic calculation. Naturally the question arises if one can modify a nonrelativistic method, say, the lowest order Brueckner theory (LOBT), to reproduce approximately the results of a relativistic calculation. While a many body effect, the role of $M^*$ is intrinsically relativistic. It cannot be simulated by adding multi-body forces in a nonrelativistic calculation. Instead, we examine if adding a set of recipes to LOBT can be useful for the purpose. We point out that the differences in the results arise principally from two reasons - first, the role of $M^*$ and second, the disappearance in a relativistic treatment of the gap in the hole and particle energy spectra, present in LOBT. In this paper we show that LOBT, modified by {\it recipes} to remove these two reasons, generates results quite close to those of Dirac-Brueckner theory., Comment: 8 pages, revtex

The recent determination of the charged $\pi NN$ coupling constant, $g_{\pi^\pm}$, by the Uppsala Neutron Research Group implies that there may be considerable charge-splitting of the pion coupling constant. We investigate the consequences of this for the charge-independence breaking (CIB) of the $^1S_0$ scattering length, $\Delta a_{CIB}$. We find that $\Delta a_{CIB}$ depends sensitively on the difference between $g_{\pi^\pm}$ and the neutral $\pi NN$ coupling constant, $g_{\pi^0}$. Moreover, if $g^2_{\pi^\pm}$ is only about 3% larger than $g^2_{\pi^0}$, then the established theoretical explanation of $\Delta a_{CIB}$ (in terms of pion mass splitting) is completely wiped out., Comment: 9 pages, fbs styles, 1 figure; dedicated to Walter Gl\"ockle on the occasion of his 60th birthday

We calculate the leading direct-instanton contributions to the operator product expansion of the nucleon correlator in a magnetic background field and set up improved QCD sum rules for the nucleon magnetic moments. Remarkably, the instanton contributions are found to affect only those sum rules which had previously been considered unstable. The new sum rules show good stability and reproduce the experimental values of the nucleon magnetic moments with values of $\chi$, the quark condensate magnetic susceptibility, consistent with other estimates., Comment: 15 pages, 2 figures