In this research paper, we have utilized the Jacobi elliptic function expansion method to obtain exact solutions of (1+1)- dimensional Boussinesq System (GBQS). The most important difference that distinguishes from other methods is parameters included in auxiliary equation F’ (ξ) = Ö P F4(ξ) + QF2(ξ) R. As far as authors know, there no study which such a variety has been given. Depending on P, ...

In this paper a new Weierstrass semi-rational expansion method is developed via the Weierstrass elliptic function ℘(ξ; g2, g3). With the aid of Maple, we choose the coupled water wave equation and the generalized Hirota-Satsuma coupled KdV equation to illustrate the method. As a consequence, it is shown that the method is powerful to obtain many types of new doubly periodic solutions in terms o...

A method is proposed for finding exact solutions of the nonlinear Schr~dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schr~dinger e...

The Benjamin-Bona-Mahony equation has improved short-wavelength behaviour, as compared to the Korteweg-de Vries equation, and is another uni-directional wave equation with cnoidal wave solutions. Cnoidal wave solutions can appear in other applications than surface gravity waves as well, for instance to describe ion acoustic waves in plasma physics. Using a computerized symbolic computation tech...

In this paper we prove identities involving the classical Jacobi theta functions of the form ∑c(i1, i2, i3, i4)θ1(z|τ)1 θ2(z|τ)2 θ3(z|τ)3 θ4(z|τ)4 = 0 with c(i1, i2, i3, i4) ∈ K[Θ], where K is a computable field and Θ := { θ 1 (0|τ) : k ∈ N } ∪ { θ j (0|τ) : k ∈ N and j = 2,3,4 } . We give two algorithms that solve this problem. The second algorithm is simpler and works in a restricted input cl...

In this article, we study for the first time stochastic Kaup–Newell equation in birefringent fibers. Three integration algorithms are applied, namely, unified Riccati expansion method, addendum to Kudryashov's and modified sub‐ODE method. Many types of optical soliton solutions such as Jacobi‐elliptic function solutions, Weierstrass elliptic bright solitons, dark singular periodic obtained. Num...

In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type, Weie...

The classical dynamics of a free particle constrained to move in an integrable two-dimensional confocal elliptic billiard is investigated. We derive the characteristic equations for periodic orbits, classify the orbits, present the Poincaré maps, give expressions for the lengths of the trajectories, and do a stability analysis of special orbits. We also explore some interesting geometrical cons...