in this paper, a fuzzy hunter-saxton equation is solved by using the adomian'sdecomposition method (adm) and homotopy analysis method (ham). theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. the existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. a nume...

In this paper, a Laplace homotopy analysis method which is based on homotopy analysis method and Laplace transform is applied to obtain the approximate solutions of fractional linear and non-linear differential equations. The proposed algorithm presents a procedure of constructing the set of base functions and gives a high-order deformation equation in simple form. Numerical examples are includ...

The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the ...

in this paper, we have tried to find a solution for quick transfer of nuclear wastes from pools of cool water to dry stores to reduce the environmental concerns and financial cost of burying atomic waste. therefore, the rate of heat transfer from atomic waste materials to the outer surface of the container should be increased. this can be achieved by covering the bottom of the pool space with c...

We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about étale homotopy types. Also, we show that cofiltered limits in pro-categories commute with finite colimits.

Floer cohomology groups are usually defined over a field of formal functions (a Novikov field). Under certain assumptions, one can equip them with connections, which means operations of differentiation with respect to the Novikov variable. This allows one to write differential equations for Floer cohomology classes. Here, we apply that idea to symplectic cohomology groups associated to Lefschet...

(1.1) H = {(x, y) ∈ (C) × C : y1y2 + p(x) = z}, Here, p : (C) → C is the superpotential mirror to Y (following [7] or [9]), and z is any regular value of p. H is an affine threefold with trivial canonical bundle. Hence, it has a Fukaya category Fuk(H), whose objects are compact exact Lagrangian submanifolds equipped with gradings and Spin structures. This is an A∞-category over C. Consider the ...

We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R3. This ‘homotopy cardinality’ is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We present an application to the augmentation category of doubly Lagrangian slice knots.

In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its comp...

Homotopy classes of trajectories, arising due to the presence of obstacles, are defined as sets of trajectories that can be transformed into each other by gradual bending and stretching without colliding with obstacles. The problem of exploring/finding the different homotopy classes in an environment and the problem of finding least-cost paths restricted to a specific homotopy class (or not bel...