We consider fifth-order nonlinear dispersive K(m,n, p) type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons the compact solitary waves free of exponential tails. This interaction also generates ma...

We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to large class Calabi-Yau geometries described by three-term operators. give two methods derive TBA-like equations. One method uses only elementary functions while other Faddeev's dilogarithm function. The approaches provide different realiza...

In this paper, we use a deep mathematical result (namely, a minor modi cation of Kolmogorov's solution to Hilbert's 13th problem) to explain why fundamental physical equations are of second order. This same result explain why all these fundamental equations naturally lead to nonsmooth solutions like singularity. Formulation of the problem. Most physical phenomena are described in terms of parti...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

In this paper, we introduced a novel variational iteration method (VIM) for solving fractional wave–like and heat–like equations in a large domain which is improved by adding an auxiliary parameter. The suggested method is very effective and we can control the convergence region very easily. By solving some fractional wave-like and heat-like equations with the proposed method and comparing with...

Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...

We consider a family of stationary Navier-Stokes ows parameterized by the Reynolds number. When the Reynolds number tends to in nity, what asymptotic behaviors are observed? This is the problem which we would like to address in the present paper. The most renowned phenomenon is the appearance of the boundary layer. This is wellknown. However, what happens in the ow region away from the boundary...

Inviscid two-dimensional (2D) fluid phenomena like hurricanes, jet streams, Jupiter’s Red Spot, and protoplanetary disks are quite common in Nature. Unfortunately, 2D fluid phenomena are difficult to study in the laboratory because the finite size of laboratory apparati commonly introduces unwanted viscous and friction effects. Magnetized electron columns, however, behave like twodimensional fl...

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained...