A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet. Two rules, the rule of solution expression and the rule of coefficient ergodicity, are proposed, which play important ...

This paper is a continuation of [MNS], where an analytic smoothing effect was proved for long-range type perturbations of the Laplacian H0 on R . In this paper, we consider short-range type perturbations H of the Laplacian on R, and we characterize the analytic wave front set of the solution to the Schrödinger equation: ef , in terms of that of the free solution: e0f , for t < 0 in the forward ...

Abstract. We give a proof of the persistence of invariant tori for analytic perturbations of isochronous systems by using the Lindstedt series expansion for the solutions. With respect to the case of anisochronous systems, there is the additional problem to find the set of allowed rotation vectors for the invariant tori, which can not given a priori simply by looking at the unperturbed system, ...

This paper is concerned with the cubic Szegő equation i∂tu = Π(|u|u), defined on the L Hardy space on the one-dimensional torus T, where Π : L(T)→ L+(T) is the Szegő projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t ∈ (−∞,∞). In addition, we find a lower bound for the radius of analyticity of the solutio...

We construct a class of analytic solutions of WZW-type open superstring field theory describing marginal deformations of a reference D-brane background. The deformations we consider are generated by on-shell vertex operators with vanishing operator products. The superstring solution exhibits an intriguing duality with the corresponding marginal solution of the bosonic string. In particular, the...

A local stability analysis is given for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. The standard linear stability analysis is reviewed, then it is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and of the one-leg fc-step numerical solutio...

We present a numerical model of two fluid mixing based on hyperbolic equations having complete state variables (velocity, pressure, temperature) for each fluid. The model is designed for the study of acceleration driven mixing layers in a chunk mix regime dominated by large scale coherent mixing structures. The numerical solution of the model is validated by comparison to the incompressible lim...

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

the objective of this article is to develop an empirically based framework for formulating and selecting a vendor in supply chain. this study applies the fuzzy set theory to evaluate the vendor selection decision. applying analytic hierarchy process (ahp) in obtaining criteria weights and applied technique for order performance by similarity to idea solution (topsis) for obtaining final ranking...