A new periodic solution to Jacobi elliptic functions of MKdV equation and BBM equation

Abstract

Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other (1+1)-dimensional and higher dimensional systems.Nonlinear partial differential equations (NPDEs) are widely used to describe phenomena in physics, biology, chemistry, and so on. Some of the most interesting features of physical systems are hidden in their nonlinear behavior, and can only be studied with appropriate methods. Over the past decades, many authors have mainly paid attention to construct various methods such as Bäcklund transformation (see [1,5,10,11,36]), Darboux transformation [36] , Inverse scattering method [10] , Hirota's bilinear method [11] , the tanh-function method [24] , the sine-cosine method [38], the homogeneous balance method [37] , symmetry reduction method (see [2, 19, 21-23, 26, 27, 29]), the geometrical method [6] , the formal variable separation approach [4] , the multilinear variable separation approach (MLVSA) [17,20] , the functional variable separation approach (FVSA) (see [30,31,39]) and the derivative-dependent functional variable separation approach (DDFVSA) [40] . Recently, an extended tanh-function method [7] and symbolic computation are used in [8] for solving the new coupled modified KdV equations to obtain four kinds of soliton solutions.The aim of this paper is to use a direct method to solve two different types of equations such as the MKdV and BBM equations.

Three Solutions to the Nonlinear Schrödinger Equation for a Constant Potential

“…Due to the method of solution, which makes use of elliptic functions, these functions will expand the set of solutions that can be given to polynomial nonlinear equations, in general [8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

A Study of Different Wave Structures of the $(2+1)$-dimensional Chiral Schrödinger Equation

“…The present article investigates different wave structures of the 2D-CS equation using the modified Kudryashov method [11][12][13][14]. This method utilizes a special finite series solution in the form [15] U…”

Soliton and other solutions to the (1 + 2)-dimensional chiral nonlinear Schrödinger equation

“…The current paper aims to present soliton and other solutions of the 2D-CNLSE using the modified Jacobi elliptic expansion (MJEE) method [7][8][9][10][11][12][13][14]. To highlight the effectiveness of the MJEE method for handling nonlinear evolution equations, a review of its recent applications is provided below.…”

“…To highlight the effectiveness of the MJEE method for handling nonlinear evolution equations, a review of its recent applications is provided below. Ma et al [7] used the MJEE method to construct new exact solutions of MKdV and BBM equations. Hosseini et al [8] obtained solitons and Jacobi elliptic function solutions of the complex Ginzburg-Landau equation using the MJEE method.…”