In this work, we employ the simple direct method to investigate the generalized mKdV equation with variable coefficients. By using this scheme, we found some new exact solutions of the equation, including four new types of Jacobi elliptic function solutions, and these solutions are degenerated to solitary wave solutions and triangle function solutions in the limit case when the modulus of the J...

(2 + 1) dimensional Boussinesq and Kadomtsev-Petviashvili equation are investigated by employing Jacobi elliptic function expansion method in this paper. As a result, some new forms traveling wave solutions of the equation are reported. Numerical simulation results are shown. These new solutions may be important for the explanation of some practical physical problems. The results of this paper ...

It is important to seek for more explicit exact solutions of nonlinear partial differential equations (NLPDEs) in mathematical physics. With the help of symbolic computation software like Maple or Mathematica, much work has been focused on the various extensions and applications of the known methods to construct exact solutions of NLPDEs. Mathematical modelling of physical systems often leads t...

For the first time, we study Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise Itô sense. Four integration algorithms are applied, namely, method of modified simple (MMSE), sine-cosine (MSC), Jacobi elliptic (MJEE) and ansatze involving hyperbolic functions. Jacobi-elliptic function solutions, bright, dark, singular, combo dark-bright bright-dark solitons ...

We study the differential equations governing mirror symmetry of elliptic curves, and obtain a characterization of the ODEs which give rise to the integral q-expansion of mirror maps. Through theta function representation of the defining equation, we express the mirror correspondence in terms of theta constants. By investigating the elliptic curves in X9-family, the identification of the Landau...

Presented are the recurrence formulas to compute the derivatives of a general elliptic function, Weierstrass’s ℘ function, the Jacobian elliptic functions, and the incomplete elliptic integrals in the forms of Jacobi and Legendre with respect to the argument or the amplitude. The double precision computation by the formulas is correct with 15 digits or so for the first 10 orders of differentiat...

A nonlinear differential equation for the polar angle of a point of an ellipse is derived. The solution of this differential equation can be expressed in terms of the Jacobi elliptic function dn u,k . If the polar angle is extended to the complex plane, the Jacobi imaginary transformation properties and the dependence on the real and complex quarter periods can be described. From the differenti...

By using solutions of an ordinary differential equation, an auxiliary equationmethod is described to seek exact solutions of variablecoefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for...

Abstract: In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions to the equation are constructed analytically under certain circumstances, some of these solutions are degenerated to soliton-like soluti...