In this paper, He’s variational iteration method (VIM) has been used to obtain solutions of the seventh-order Sawada-Kotera equation (sSK) and a Lax’s seventh order KdV equations(LsKdV).The numerical solutions are compared with the Adomian decomposition method(ADM) and the known analytical solutions.The work confirms the power of the VIM in reducing the size of calculations w.r.t. ADM. Some ill...

This paper focuses on solving the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation (FCDGSKE). We propose two analytical methods based complex transform, variational iteration method and homotopy perturbation method. The approximated solutions to initial value problems associated with FCDGSKE are provided without linearization complicated calculation. Numerical results show main merits...

A math e mat i cal model rep re sent ing tem per a ture and mois ture con tent in bread dur ing bak ing is de vel oped. The model em ploys the cou pled par tial dif fer en tial equa tions pro posed by Luikov. Dependences of mass and ther mal prop er ties of dough on tem per a ture and mois ture con tent are in cluded in the model. Re sult ing sys tem of non-lin ear par tial dif fer en tial equa...

The recently detected inertial effect on the behaviour of the fluorescence anisotropy r = \ j /J — \ as a function of the viscosity rj of a solvent for prolate luminescent molecule, the transition moment of which lies along its longer axis (see [1,2] and refs. quoted there), was explained using the non-Markovian generalized d i f fus ion equat ion [1], The a im of the present note is to extend ...

1. Introduction Piecewise linear algorithms, also referred to in the literature as sim-plicial algorithms, can be used to generate piecewise linear manifolds which approximate the solutions of underdetermined systems of equa

E. Abouzaid, M. Arenton, A.R. Barker, ∗ L. Bellantoni, E. Blucher, G.J. Bock, E. Cheu, R. Coleman, M.D. Corcoran, B. Cox, A.R. Erwin, C.O. Escobar, A. Glazov, A. Golossanov, R.A. Gomes, P. Gouffon, Y.B. Hsiung, D.A. Jensen, R. Kessler, K. Kotera, A. Ledovskoy, P.L. McBride, E. Monnier, † H. Nguyen, R. Niclasen, D.G. Phillips II, E.J. Ramberg, R.E. Ray, M. Ronquest, E. Santos, W. Slater, D. Smit...

We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kote...

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New potentials and corresponding solutions of the Sawada–Kotera, Kaup– Kupershmidt, Boussinesq eq...

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...