The weak Neumann problem for the Poisson eqution is studied on Lipschitz domain with compact boundary using the direct integral equation method. The domain is bounded or unbounded, the boundary might be disconnected. The problem leads to a uniquely solvable integral equation in H(∂Ω). It is proved that we can get the solution of this equation using the successive approximation method. AMS class...

We give a systematic account of isospectral deformations for Sturm-Liouville and Dirac-type operators and associated hierarchies of nonlinear evolution equations. In particular, we study generalized KdV and modified KdV-hierarchies and their reduction to the standard (m)KdV-hierarchy. As an example we study the Harry Dym equation in some detail and relate its solutions to KdV-solutions and to H...

A new transformation v=4(lnf)xx that can formulate a quintic linear equation and pair of Hirota’s bilinear equations for the (2 + 1)-dimensional Sawada–Kotera (2DSK) Eq. (1) or u=4(lnf)x 2DSK (2) is reported firstly, which enables one to obtain set multiple soliton solutions equation. They are not special cases known solitons. The results presented in this paper show only possesses two sets sol...

in this paper, an analytical method called the parametric iteration method (pim) is presented for solving the second-order singular ivps of lane-emden type, and its local convergence is discussed. since it is often useful to have an approximate analytical solution to describe the lane-emden type equa- tions, especially for ones where the closed-form solutions do not exist at all, therefore, an ...

E. Abouzaid, M. Arenton, A.R. Barker, ∗ L. Bellantoni, A. Bellavance, 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, H. Ping, E.J. Ramberg, R.E. Ray, M. Ronquest, E. ...

This study investigates the wave solutions of time-fractional Sawada–Kotera–Ito equation (SKIE) that arise in shallow water and many other fluid mediums by utilizing some most flexible high-precision methods. The SKIE is a nonlinear integrable partial differential (PDE) with significant applications dynamics mechanics. However, traditional numerical methods used for analyzing this are often pla...

Symbolic pattern solving is a new approach for nding symbolic solutions of equa-tional constraints over arbitrary algebraic structures. Despite the deep results and methods already produced in equational constraint solving, real-world applications still cannot be tackled. To reduce the original complexity, the approach advocated here uses the solution pattern, the skeleton of the solution often...

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space R .

The Douglas–Rachford and Peaceman–Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract re...