Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2 + 1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitr...

We derive rigorously, for both R and [−L,L], the cubic nonlinear Schrödinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cub...

The theory of phase-shifted nonlinear periodic structures operating in the stationary regime is presented. The transmissive properties of the structure are analyzed by solution of the corresponding set of nonlinear coupledmode equations exactly. Extremely low switching intensities are found for the special case of ly4-shifted structures. An all-optical low-intensity switching configuration that...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

The relative motion of an outline the rendezvous problem has been studied by assuming that chief satellite is in circular symmetric orbits. legitimacy perturbation techniques and nonlinear are investigated. deputy equations with respect to fixed references at center general case. We found periodic solutions linear for using Lindstedt–Poincaré technique. Comparisons among analytical motions obta...

in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

We consider a class of nonlinear Fokker–Planck equations describing the dynamics an infinite population units with mean-field interaction. Relying on slow–fast viewpoint and theory approximately invariant manifolds we obtain existence stable periodic solution for PDE, consisting probability measures. Moreover establish smooth isochron map in neighborhood this solution.