In this manuscript, the Cauchy problem of modified Helmholtz equation is researched. This inverse a serious ill-posed problem. The classical Landweber iterative regularization method designed to find regularized solution error estimations between exact and are all obtained under priori posteriori parameter selection rule. can also be applied solve on spherically symmetric cylindrically regions.

We are concerned with the long-time asymptotic behavior of solution for focusing Hirota equation (also called third-order nonlinear Schrödinger equation) symmetric, non-zero boundary conditions (NZBCs) at infinity. Firstly, based on Lax pair NZBCs, direct and inverse scattering problems used to establish oscillatory Riemann-Hilbert (RH) problem distinct jump curves. Secondly, Deift-Zhou steepes...

applying the variational method, the spinless reduced bethe-salpeter (rbs) equation is solved for the mesonic systems, and the mass spectra are obtained. the method is applied to the hamiltonian with the gaussian and hydrogen-type trial wave functions, and different potential models are examined. the results for the different potentials are in challenge in light mesons, while they are consisten...

Abstract We study integrability properties of the non-chiral intermediate long wave equation recently introduced by authors as a parity-invariant variant equation. For this new we: (a) derive Lax pair, (b) Hirota bilinear form, (c) Bäcklund transformation, (d) use, separately, transformation and representation to obtain an infinite number conservation laws.

We construct a gauge theoretic change of variables for the wave map from R × R into a compact group or Riemannian symmetric space, prove a new multiplication theorem for mixed Lebesgue-Besov spaces, and show the global well-posedness of a modified wave map equation n ≥ 4 for small critical initial data. We obtain global existence and uniqueness for the Cauchy problem of wave maps into compact L...

The main goal of the current work is to develop numerical approaches that use Yang transform, homotopy perturbation method (HPM), and Adomian decomposition analyze fractional model regularized long-wave equation. shallow-water waves ion-acoustic in plasma are both explained by first combines transform with He’s polynomials. In contrast, second polynomials method. Caputo sense applied derivative...