We present a review of results of the so-called Painlevé singularity approach to the
investigation of the integrability of dynamical systems with finite and infinite number of …

We discuss the direct methods that can be used to search for the second invariant of a
system defined by the Hamiltonian H= 1 2 (px 2)+ py 2+ A (x, y) p x+ B (x, y) p y+ V (x, y). We …

The present work studies one of Einstein's alternative formulations based on the
nonmetricity scalar Q generalized as f (Q) theory. More specifically, we consider the power …

There has been a revolution in nonlinear physics over the past twenty years. Two great
discoveries, each of which, incidentally, was made with the aid of the computer experiment …

Some new similarity reductions of the Boussinesq equation, which arises in several physical
applications including shallow water waves and also is of considerable mathematical …

It is known through the inverse scattering transform that certain nonlinear differential
equations can be solved via linear integral equations. Here it is demonstrated" directly," ie …

We establish the local well‐posedness of a recently derived model for small‐amplitude,
shallow water waves. For a large class of initial data we prove global existence of the …

The particle paths of the Arnold-Beltrami-Childress (ABC) flows\[u=(A\sin z+ C\cos y, B\sin x+
A\cos z, C\sin y+ B\cos x).\] are investigated both analytically and numerically. This three …

The quantal system of Bose particles described by the non-linear Schrödinger equation i∂
φ/∂ t=-1 2∂ 2 φ/∂ x 2+ cφ∗ φ 2, with c= cxf∞ and via the ground state with finite particle …

We consider the evolution of packets of water waves that travel predominantly in one
direction, but in which the wave amplitudes are modulated slowly in both horizontal …