Influence of Injection/Suction on Mixed Convection Flow Across a Vertical Cone Saturated Porous Medium with Double Dispersion and Chemical Reaction Effects

We examined how injection/suction impacts the flow characteristics for mixed convection across a vertical cone saturated porous medium in the presence of double dispersion and chemical reaction effects. We perform suitable transformations to convert the nonlinear system of partial differential expressions into a system of non-dimensional form and received dimensionless equations solved numerically by the bivariate Chebyshev spectral collocation quasi-linearization method. We explain the outcomes of the flow characteristics over various variables through diagrams and numerical benchmarks. We also establish precision verification of the chosen numerical technique through a comparison with prior published computations and found to be in great assent. The residual analysis section also illustrated which unblocks convergence of the present results.

Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

The D∗Dπ and B∗Bπ couplings from light-cone sum rules

We revisit the calculation of the strong couplings D∗Dπ and B∗Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict $$ {g}_{D^{\ast } D\pi}={14.1}_{-1.2}^{+1.3} $$ g D ∗ Dπ = 14.1 − 1.2 + 1.3 and $$ {g}_{B^{\ast } B\pi}={30.0}_{-2.4}^{+2.6} $$ g B ∗ Bπ = 30.0 − 2.4 + 2.6 when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

Conservation Laws and Travelling Wave Solutions for Double Dispersion Equations in (1+1) and (2+1) Dimensions

In this article, we investigate two types of double dispersion equations in two different dimensions, which arise in several physical applications. Double dispersion equations are derived to describe long nonlinear wave evolution in a thin hyperelastic rod. Firstly, we obtain conservation laws for both these equations. To do this, we employ the multiplier method, which is an efficient method to derive conservation laws as it does not require the PDEs to admit a variational principle. Secondly, we obtain travelling waves and line travelling waves for these two equations. In this process, the conservation laws are used to obtain a triple reduction. Finally, a line soliton solution is found for the double dispersion equation in two dimensions.