The Painlevé equations and their solutions occur in some areas of theoretical physics, pure
and applied mathematics. This paper applies natural decomposition method (NDM) and …

In this paper, novel computing approach using three different models of feed-forward
artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) …

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic
splines method (CSM) has been utilized to estimate the numerical results of nonlinear …

In this paper, a reliable soft computing framework is presented for the approximate solution
of initial value problem (IVP) of first Painlevé equation using three unsupervised neural …

The Painlevé-Calogero correspondence is extended to auxiliary linear problems associated
with Painlevé equations. The linear problems are represented in a new form which has a …

We obtain the strong asymptotics of polynomials p_n (λ) pn (λ), λ ∈ C λ∈ C, orthogonal with
respect to measures in the complex plane of the form e^-N (| λ|^ 2s-t λ^ st λ^ s) d A (λ), eN …

In this study, we introduce a new approximative algorithm to get numerical solutions of the
nonlinear first Painlevé equation. Indeed, to obtain an approximate solution, a combination …

We study the equilibrium measure on the two-dimensional sphere in the presence of an
external field generated by r+ 1 equal point charges that are symmetrically located around …

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems
considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two …

In light of the quantum Painlevé–Calogero correspondence, we investigate the inverse
problem. We imply that this type of the correspondence (classical-quantum correspondence) …