In this paper, the twisted Jacobi intersections which contains Jacobi intersections as a special case is introduced. We show that every elliptic curve over the prime field with three points of order 2 is isomorphic to a twisted Jacobi intersections curve. Some fast explicit formulae for twisted Jacobi intersections curves in projective coordinates are presented. These explicit formulae for addi...

A generalized (G ′ /G)-expansion method is used to search for the exact traveling wave solutions of the coupled KdV-mKdV equation. As a result, some new Jacobi elliptic function solutions are obtained. It is shown that the method is straightforward, concise, effective, and can be used for many other nonlinear evolution equations in mathematical physics.

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...

We mainly construct and analyze the multi elliptic-localized solutions under background of elliptic function for focusing modified Korteweg-de Vries (mKdV) equation. Based on Darboux–Bäcklund transformation, we provide a uniform expression these by Jacobi theta functions. The asymptotic behaviors are provided directly in two categories. By consistent those solutions, obtain that collisions betw...

The Fokas system with M-truncated derivative (FS-MTD) was considered in this study. To get analytical solutions of FS-MTD the forms elliptic, rational, hyperbolic, and trigonometric functions, we employed extend F-expansion approach Jacobi elliptic function method. Since nonlinear pulse transmission monomode optical fibers is explained by system, derived may be utilized to analyze a broad range...

In this paper, we use two different integral techniques, the first integral and the direct integral method, to study the variable coefficient nonlinear Schrödinger (NLS) equation arising in arterial mechanics. The application of the first integral method yielded periodic and solitary wave solutions. Using the direct integration lead to solitary wave solution and Jacobi elliptic function solutions.

A collocation-//"'-Galerkin method is defined for some elliptic boundary value problems on a rectangle. The method uses tensor products of discontinuous piecewise polynomial spaces and collocation based on Jacobi points with weight function >c2(l x)2. Optimal order of L2 rates of convergence is established for the approximation solution. A numerical example which confirms these results is prese...

We investigate the dynamics of an inverted pendulum subjected to Jacobi elliptic forcing both numerically and experimentally. In so doing, we hope to provide a coherent picture on stability of an inverted pendulum subjected to forcing that ranges from harmonic to nonharmonic in nature. We are able to determine the regions of stability of a sinusoidally forced inverted pendulum, with results sim...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

The paper is concerned with fully nonlinear second order Hamilton{Jacobi{Bellman{ Isaacs equations of elliptic type in separable Hilbert spaces which have unbounded rst and second order terms. The viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions is proved. A stochastic optimal control problem driven by a paraboli...