The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use multi-layer PINN learning method study data-driven rogue wave solutions defocusing Schr\"odinger (NLS) equation with time-dependent potential by considering several initial conditions such as wave, Jacobi elliptic cosine fu...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

In this work,The free nonlinear vibrations of nanotubes using the Euler-Bernoulli beam theory along with the von Kármán geometric nonlinearity in presence of surface effects has been investigated. Natural frequencies of a simply-supported nanotube in terms of the Jacobi elliptic functions are obtained by using the free vibration modes of the corresponding linear problem. The numerical results d...

Elliptic functions have been known for about 150 years, mainly through the work of the mathematicians Legendre, Abel, and most of all, C. G. J. Jacobi ~1804–1851!. They are doubly periodic functions of a variable in the complex plane with the additional property that they are meromorphic, i.e., they have only poles as singularities. Among the elliptic functions, the so-called Jacobian elliptic ...

In this paper we study the motion of photons or massless particles in $C$ metric with cosmological constant. The Hamilton-Jacobi equations are known to be completely separable, giving a Carter-like quantity $Q$ which is constant motion. All possible trajectories classified according two-dimensional parameter space representing particle's angular momentum and energy scaled units $Q$. Exact solut...

Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons other exact solutions through birefringent fibers for Biswas–Arshed equation with multiplicative white noise using modified extended mapping method. model contains many kinds soliton solutions, which are always symmetric or anti-symm...

In this article, the generalized Jacobi elliptic function expansion method with four new functions was used to fractional (3 + 1)-dimensional Kadomtsev–Petviashvili (GFKP) equation Atangana-Baleanu-Riemann derivative, and abundant types of analytical solutions GFKP were obtained. It is well known that there a tight connection between symmetry travelling wave solutions. Most existing techniques ...

Efficiently direct solvers based on the Jacobi–Galerkin method for the integrated forms of second-order elliptic equations in one and two space variables are presented. They are based on appropriate base functions for the Galerkin formulation which lead to discrete systems with specially structured matrices that can be efficiently inverted. The homogeneous Dirichlet boundary conditions are sati...